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Artykuły w czasopismach na temat „Stochastic Fokker-Planck”

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Data publikacji: 14 grudnia 2024

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1

Liu, Chang, Chuo Chang i Zhe Chang. "Distribution of Return Transition for Bohm-Vigier Stochastic Mechanics in Stock Market". Symmetry 15, nr 7 (17.07.2023): 1431. http://dx.doi.org/10.3390/sym15071431.

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The Bohm-Vigier stochastic model is assumed as a natural generalization of the Black-Scholes model in stock market. The behavioral factor of stock market recognizes as a hidden sector in Bohmian mechanics. A Fokker-Planck equation description for the Bohm-Vigier stochastic model is presented. We find the familiar Boltzmann distribution is a stationary solution of the Fokker-Planck equation for the Bohm-Vigier model. The return transition distribution of stock market, which corresponds with a time-dependent solution of the Fokker-Planck equation, is obtained.

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2

Coghi, Michele, i Benjamin Gess. "Stochastic nonlinear Fokker–Planck equations". Nonlinear Analysis 187 (październik 2019): 259–78. http://dx.doi.org/10.1016/j.na.2019.05.003.

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Chavanis, Pierre-Henri. "Generalized Stochastic Fokker-Planck Equations". Entropy 17, nr 5 (13.05.2015): 3205–52. http://dx.doi.org/10.3390/e17053205.

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4

Lin, Y. K., i G. Q. Cai. "Equivalent Stochastic Systems". Journal of Applied Mechanics 55, nr 4 (1.12.1988): 918–22. http://dx.doi.org/10.1115/1.3173742.

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Equivalent stochastic systems are defined as randomly excited dynamical systems whose response vectors in the state space share the same probability distribution. In this paper, the random excitations are restricted to Gaussian white noises; thus, the system responses are Markov vectors, and their probability densities are governed by the associated Fokker-Planck equations. When the associated Fokker-Planck equations are identical, the equivalent stochastic systems must share both the stationary probability distribution and the transient nonstationary probability distribution under identical initial conditions. Such systems are said to be stochastically equivalent in the strict (or strong) sense. A wider class, referred to as the class of equivalent stochastic systems in the wide (or weak) sense, also includes those sharing only the stationary probability distribution but having different Fokker-Planck equations. Given a stochastic system with a known probability distribution, procedures are developed to identify and construct equivalent stochastic systems, both in the strict and in the wide sense.

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5

KOTELENEZ, PETER M. "A QUASI-LINEAR STOCHASTIC FOKKER–PLANCK EQUATION IN σ-FINITE MEASURES". Stochastics and Dynamics 08, nr 03 (wrzesień 2008): 475–504. http://dx.doi.org/10.1142/s021949370800241x.

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Solutions of quasi-linear stochastic Fokker–Planck equations for the number density of a system of solute particles in suspension are derived. The initial values and the solutions take values in a class of σ-finite Borel measures over Rd where d ≥ 1. The stochastic driving noise is defined by Itô differentials. For the special case of semi-linear stochastic Fokker–Planck equations, the solutions can be represented as solutions of first-order stochastic transport equations driven by Stratonovich differentials.

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6

Sun, Xu, Xiaofan Li i Yayun Zheng. "Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise". Stochastics and Dynamics 17, nr 05 (23.09.2016): 1750033. http://dx.doi.org/10.1142/s0219493717500332.

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Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs in arbitrary dimensions driven by non-Gaussian Lévy processes. The equations are given in a simple form that facilitates theoretical analysis and numerical computation. Several examples are presented to illustrate how the theoretical results can be applied to obtain Fokker–Planck equations for Marcus SDEs driven by Lévy processes.

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7

Hirpara, Ravish Himmatlal, i Shambhu Nath Sharma. "An Analysis of a Wind Turbine-Generator System in the Presence of Stochasticity and Fokker-Planck Equations". International Journal of System Dynamics Applications 9, nr 1 (styczeń 2020): 18–43. http://dx.doi.org/10.4018/ijsda.2020010102.

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In power systems dynamics and control literature, theoretical and practical aspects of the wind turbine-generator system have received considerable attentions. The evolution equation of the induction machine encompasses a system of three first-order differential equations coupled with two algebraic equations. After accounting for stochasticity in the wind speed, the wind turbine-generator system becomes a stochastic system. That is described by the standard and formal Itô stochastic differential equation. Note that the Itô process is a strong Markov process. The Itô stochasticity of the wind speed is attributed to the Markov modeling of atmospheric turbulence. The article utilizes the Fokker-Planck method, a mathematical stochastic method, to analyse the noise-influenced wind turbine-generator system by doing the following: (i) the authors develop the Fokker-Planck model for the stochastic power system problem considered here; (ii) the Fokker-Planck operator coupled with the Kolmogorov backward operator are exploited to accomplish the noise analysis from the estimation-theoretic viewpoint.

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8

Annunziato, Mario, i Alfio Borzì. "OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES". Mathematical Modelling and Analysis 15, nr 4 (15.11.2010): 393–407. http://dx.doi.org/10.3846/1392-6292.2010.15.393-407.

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A Fokker‐Planck framework for the formulation of an optimal control strategy of stochastic processes is presented. Within this strategy, the control objectives are defined based on the probability density functions of the stochastic processes. The optimal control is obtained as the minimizer of the objective under the constraint given by the Fokker‐Planck model. Representative stochastic processes are considered with different control laws and with the purpose of attaining a final target configuration or tracking a desired trajectory. In this latter case, a receding‐horizon algorithm over a sequence of time windows is implemented.

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9

ANNUNZIATO, M., i A. BORZI. "FOKKER–PLANCK-BASED CONTROL OF A TWO-LEVEL OPEN QUANTUM SYSTEM". Mathematical Models and Methods in Applied Sciences 23, nr 11 (23.07.2013): 2039–64. http://dx.doi.org/10.1142/s0218202513500255.

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The control of a two-level open quantum system subject to dissipation due to environment interaction is considered. The evolution of this system is governed by a Lindblad master equation which is augmented by a stochastic term to model the effect of time-continuous measurements. In order to control this stochastic master equation model, a Fokker–Planck control framework is investigated. Within this strategy, the control objectives are defined based on the probability density functions of the two-level stochastic process and the controls are computed as minimizers of these objectives subject to the constraints represented by the Fokker–Planck equation. This minimization problem is characterized by an optimality system including the Fokker–Planck equation and its adjoint. This optimality system is approximated by a second-order accurate, stable, conservative and positive-preserving discretization scheme. The implementation of the resulting open-loop controls is realized with a receding-horizon algorithm over a sequence of time windows. Results of numerical experiments demonstrate the effectiveness of the proposed approach.

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10

RENNER, CHRISTOPH, J. PEINKE i R. FRIEDRICH. "Experimental indications for Markov properties of small-scale turbulence". Journal of Fluid Mechanics 433 (25.04.2001): 383–409. http://dx.doi.org/10.1017/s0022112001003597.

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We present a stochastic analysis of a data set consisting of 1.25 × 107 samples of the local velocity measured in the turbulent region of a round free jet. We find evidence that the statistics of the longitudinal velocity increment v(r) can be described as a Markov process. This new approach to characterize small-scale turbulence leads to a Fokker–Planck equation for the r-evolution of the probability density function (p.d.f.) of v(r). This equation for p(v, r) is completely determined by two coefficients D1(v, r) and D2(v, r) (drift and diffusion coefficient, respectively). It is shown how these coefficients can be estimated directly from the experimental data without using any assumptions or models for the underlying stochastic process. The solutions of the resulting Fokker–Planck equation are compared with experimentally determined probability density functions. It is shown that the Fokker–Planck equation describes the measured p.d.f.(s) correctly, including intermittency effects. Furthermore, knowledge of the Fokker–Planck equation also allows the joint probability density of N increments on N different scales p(v1, r1, …, vN, rN) to be determined.

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11

PELETIER, MARK A., D. R. MICHIEL RENGER i MARCO VENERONI. "VARIATIONAL FORMULATION OF THE FOKKER–PLANCK EQUATION WITH DECAY: A PARTICLE APPROACH". Communications in Contemporary Mathematics 15, nr 05 (30.09.2013): 1350017. http://dx.doi.org/10.1142/s021919971350017x.

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We introduce a stochastic particle system that corresponds to the Fokker–Planck equation with decay in the many-particle limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Mosco-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is again a variational formulation for the Fokker–Planck equation with decay.

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12

Maoutsa, Dimitra, Sebastian Reich i Manfred Opper. "Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation". Entropy 22, nr 8 (22.07.2020): 802. http://dx.doi.org/10.3390/e22080802.

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Fokker–Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker–Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker–Planck equations in low and moderate dimensions. The proposed gradient–log–density estimator is also of independent interest, for example, in the context of optimal control.

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13

Zhang, Yutian, i Feng Chen. "Stochastic stability of fractional Fokker–Planck equation". Physica A: Statistical Mechanics and its Applications 410 (wrzesień 2014): 35–42. http://dx.doi.org/10.1016/j.physa.2014.05.012.

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14

Xu, Chaoqun, i Sanling Yuan. "Richards Growth Model Driven by Multiplicative and Additive Colored Noises: Steady-State Analysis". Fluctuation and Noise Letters 19, nr 04 (29.05.2020): 2050032. http://dx.doi.org/10.1142/s0219477520500327.

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We consider a Richards growth model (modified logistic model) driven by correlated multiplicative and additive colored noises, and investigate the effects of noises on the eventual distribution of population size with the help of steady-state analysis. An approximative Fokker–Planck equation is first derived for the stochastic model. By performing detailed theoretical analysis and numerical simulation for the steady-state solution of the Fokker–Planck equation, i.e., stationary probability distribution (SPD) of the stochastic model, we find that the correlated noises have complex effects on the statistical property of the stochastic model. Specifically, the phenomenological bifurcation may be caused by the noises. The position of extrema of the SPD depends on the model parameter and the characters of noises in different ways.

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15

MOCHIZUKI, RIUJI. "QUANTUM EFFECT AND OPERATOR ORDERING IN STOCHASTIC HAMILTONIAN". Modern Physics Letters A 06, nr 02 (20.01.1991): 117–21. http://dx.doi.org/10.1142/s0217732391000051.

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We investigate the operator ordering in the stochastic Hamiltonian in a generalized stochastic calculation method. It is uniquely determined in the continuum limit and yields the Fokker-Planck equation without dependence on the calculation method.

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16

Annunziato, Mario, i Alfio Borzì. "Fokker–Planck Analysis of Superresolution Microscopy Images". Mathematical and Computational Applications 28, nr 6 (14.12.2023): 113. http://dx.doi.org/10.3390/mca28060113.

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A method for the analysis of super-resolution microscopy images is presented. This method is based on the analysis of stochastic trajectories of particles moving on the membrane of a cell with the assumption that this motion is determined by the properties of this membrane. Thus, the purpose of this method is to recover the structural properties of the membrane by solving an inverse problem governed by the Fokker–Planck equation related to the stochastic trajectories. Results of numerical experiments demonstrate the ability of the proposed method to reconstruct the potential of a cell membrane by using synthetic data similar those captured by super-resolution microscopy of luminescent activated proteins.

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17

FAN, ZHONGHUI, i SIMING LIU. "STOCHASTIC ELECTRON ACCELERATION IN SNR RX J1713.7-3946". International Journal of Modern Physics: Conference Series 23 (styczeń 2013): 319–23. http://dx.doi.org/10.1142/s2010194513011550.

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Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in the energy space with the Fokker-Planck equation. In this paper, a time-dependent numerical code is used to solve the reduced Fokker-Planck equation involving only time and energy variables with general forms of the diffusion coefficients. We also propose a self-similar model for particle acceleration in Sedov explosions and use the TeV SNR RX J1713.7-3946 as an example to demonstrate the model characteristics. Markov Chain Monte Carlo method is utilized to constrain model parameters with observations.

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18

Yanishevskyi, V. S., i L. S. Nodzhak. "Fractional Brownian motion in financial engineering models". Mathematical Modeling and Computing 10, nr 2 (2023): 445–57. http://dx.doi.org/10.23939/mmc2023.02.445.

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An application of fractional Brownian motion (fBm) is considered in stochastic financial engineering models. For the known Fokker–Planck equation for the fBm case, a solution for transition probability density for the path integral method was built. It is shown that the mentioned solution does not result from the Gaussian unit of fBm with precise covariance. An expression for approximation of fBm covariance was found for which solutions are found based on the Gaussian measure of fBm and those found based on the known Fokker–Planck equation match.

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19

Annunziato, Mario, i Alfio Borzi. "A Fokker–Planck control framework for stochastic systems". EMS Surveys in Mathematical Sciences 5, nr 1 (18.06.2018): 65–98. http://dx.doi.org/10.4171/emss/27.

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20

De Moor, Sylvain, Luis Miguel Rodrigues i Julien Vovelle. "Invariant measures for a stochastic Fokker-Planck equation". Kinetic & Related Models 11, nr 2 (2018): 357–95. http://dx.doi.org/10.3934/krm.2018017.

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21

Hu Gang, G. Nicolis i C. Nicolis. "Periodically forced Fokker-Planck equation and stochastic resonance". Physical Review A 42, nr 4 (1.08.1990): 2030–41. http://dx.doi.org/10.1103/physreva.42.2030.

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22

Baili, Hana. "Hybrid stochastic differential systems in pharmacokinetics". IMA Journal of Mathematical Control and Information 39, nr 1 (7.12.2021): 22–59. http://dx.doi.org/10.1093/imamci/dnab034.

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Abstract Modelling patient medication poor compliance combined with the inherent uncertainty in a bioavailability trial leads recognizably to the fact that plasma concentration-time curve must be treated as a random process. We suggest for modelling a general class of hybrid stochastic differential systems (HSDS). Roughly speaking, a HSDS is a piecewise diffusion process with jumps of two types: spontaneous and predictable. The essential tasks for us afterwards are to identify the model ingredients and to derive its bearings; of interest are a couple of operators associated to every Markov process: the generating operator and the Fokker–Planck operator. The model induces a Fokker–Planck–Kolmogorov equation along with moment equations, and computations based on direct solutions of the latter make it possible to study the variability of the concentration around its mean as compared to the full compliance case and to assess the effect of some parameters such as the intake and elimination rates.

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23

Luo, Chaoliang, i Shangjiang Guo. "Stability and Bifurcation of a Class of Stochastic Closed Orbit Equations". International Journal of Bifurcation and Chaos 25, nr 11 (październik 2015): 1550148. http://dx.doi.org/10.1142/s0218127415501485.

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In this paper, by using Lyapunov functions and exponents, Feller's scale functions, and the Fokker–Planck equations, we investigate the stability and bifurcation of stochastic closed orbit equations with singular diffusion coefficients.

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24

POTOTSKY, A., i N. JANSON. "GLOBAL DYNAMICS IN NETWORKS OF 1D ELEMENTS WITH TIME DELAYED MEAN FIELD COUPLING SUBJECT TO NOISE: SYNCHRONIZATION THRESHOLD, MULTISTABILITY AND HYSTERESIS". International Journal of Bifurcation and Chaos 20, nr 06 (czerwiec 2010): 1825–36. http://dx.doi.org/10.1142/s0218127410026873.

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We determine the boundary of the synchronization domain of a large number of one-dimensional continuous stochastic elements with time delayed nonhomogeneous mean-field coupling. The exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker–Planck equation. Here the synchronization threshold is found by solving this BVP using the continuation technique (AUTO). Approximate analytics is obtained using expansion into eigenfunctions of the stationary Fokker–Planck operator. Multistability and hysteresis are demonstrated for the case of bistable elements with a polynomial potential.

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25

Acebron, J., Dr Bulsara i W. J. Rappel. "Dynamics оf globally coupled noisy FitzHugh-Nagumo neuron elements". Izvestiya VUZ. Applied Nonlinear Dynamics 11, nr 3 (31.12.2003): 110–19. http://dx.doi.org/10.18500/0869-6632-2003-11-3-110-119.

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We study the noisy FitzHugh-Nagumo model in the presence оf аn external sinusoidal driving force. We derive a Fokker-Planck equation for both the single element and for the globally coupled system. We introduce аn efficient way to numerically solve this Fokker-Planck equation and show that the external driving force leads to a classical resonance when its frequency matches the underlying systems frequency. This resonance is also investigated analytically by exploiting the different timescales in the problem. Agreement between the analytical results and numerical results is excellent and reveals the existence оf а stochastic bifurcation.

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26

NARDULLI, G., i L. TEDESCO. "PARITY-VIOLATING ANOMALY FROM THE FOKKER-PLANCK EQUATION". Modern Physics Letters A 06, nr 02 (20.01.1991): 123–28. http://dx.doi.org/10.1142/s0217732391000063.

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We compute parity-violating anomaly in gauge theories with odd number of dimensions using an approach based on the effective Fokker-Planck equation in the stochastic quantization scheme. We find results that agree with those obtained by the Langevin equation.

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27

McMillan, Stephen L. W., i Kimberly A. Engle. "Are Gravothermal Oscillations Gravothermal?" Symposium - International Astronomical Union 174 (1996): 379–80. http://dx.doi.org/10.1017/s0074180900001911.

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We examine critically the properties of the large-amplitude oscillations seen in Fokker-Planck simulations of globular clusters, with both continuous and stochastic binary heating, and compare them to the defining characteristics of gravothermal oscillations.

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28

DE MARTINO, SALVATORE, SILVIO DE SIENA, GIUSEPPE VITIELLO i FABRIZIO ILLUMINATI. "DIFFUSION PROCESSES AND COHERENT STATES". Modern Physics Letters B 08, nr 16 (10.07.1994): 977–84. http://dx.doi.org/10.1142/s0217984994000984.

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It is shown that uncertanity relations, as well as coherent and squeezed states, are structural properties of stochastic processes with Fokker–Planck dynamics. The quantum mechanical coherent and squeezed states are explicitly constructed via Nelson stochastic quantization. The method is applied to derive new minimum uncertainty states in time-dependent oscillator potentials.

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29

Carrillo, José A., Young-Pil Choi i Samir Salem. "Propagation of chaos for the Vlasov–Poisson–Fokker–Planck equation with a polynomial cut-off". Communications in Contemporary Mathematics 21, nr 04 (31.05.2019): 1850039. http://dx.doi.org/10.1142/s0219199718500396.

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We consider a [Formula: see text]-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like [Formula: see text] with [Formula: see text] in the force, we provide a quantitative error estimate between the empirical measure associated to that [Formula: see text]-particle system and the solutions of the [Formula: see text]-dimensional Vlasov–Poisson–Fokker–Planck (VPFP) system. We also study the propagation of chaos for the Vlasov–Fokker–Planck equation with less singular interaction forces than the Newtonian one.

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30

Gültekin, Özgür, Çağatay Eskin i Esra Yazicioğlu. "Deterministic and Stochastic Research of Cubic Population Model with Harvesting". Fluctuation and Noise Letters 20, nr 03 (18.01.2021): 2150023. http://dx.doi.org/10.1142/s0219477521500231.

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A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

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31

Shakeri, Ehsan, Gholamreza Latif-Shabgahi i Amir Esmaeili Abharian. "Design of an intelligent stochastic model predictive controller for a continuous stirred tank reactor through a Fokker-Planck observer". Transactions of the Institute of Measurement and Control 40, nr 10 (26.06.2017): 3010–22. http://dx.doi.org/10.1177/0142331217712583.

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Over the years, different methods have been presented to control continuous stirred tank reactors (CSTRs) in which stochastic behavior of process has rarely been considered. This article uses the stochastic model of CSTR to compute the temperature of coolant as process input in order to control the joint probability density function (PDF) of process concentration and temperature. The computation is carried out based on receding horizon-model predictive control (RH-MPC). Since observer has important role in the determination of process input, we use a nonlinear stochastic Fokker-Planck observer to calculate process PDF. The CSTR model is nonlinear and complex, so the particle swarm optimization (PSO) algorithm is used for simplification of computations and for determination of the optimal value of process input. For this purpose, an MPC problem is described for which the cost function is defined based on the difference between the process PDF and a desired PDF. In this definition, temperature limitation of the coolant and the corresponding Fokker-Planck equation are both assumed as the problem constraints. When this MPC problem is solved by the use of PSO, the process input is calculated for each time window. The existence and uniqueness of our optimal solution is also studied. In the article, the Fokker-Planck equation for CSTR model will be solved by the use of path integral method. In this way, the joint PDF of process concentration and temperature is obtained for any instance of time. The simulation results are also obtained to evaluate the proposed method.

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32

Ha, Seung-Yeal, Myeongju Kang, Dohyun Kim, Jeongho Kim i Insoon Yang. "Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence". Mathematical Models and Methods in Applied Sciences 32, nr 03 (26.02.2022): 533–617. http://dx.doi.org/10.1142/s0218202522500130.

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We study a consensus-based method for minimizing a nonconvex function over the Stiefel manifold. The consensus dynamics consists of stochastic differential equations for interacting particle system, whose trajectory is guaranteed to stay on the Stiefel manifold. For the proposed model, we prove the mean-field limit of the stochastic system toward a nonlinear Fokker–Planck equation on the Stiefel manifold. Moreover, we provide a sufficient condition on the parameter and the initial data, so that the solution to the Fokker–Planck equation is asymptotically concentrated on the point near a global optimizer. To implement our consensus-based optimization (CBO) algorithm, we provide two algorithms; one is improved from the algorithm suggested in our previous work, and the other is based on an entirely different approach, namely the Cayley transformation. We validate the CBO algorithms on the various test problems on the Stiefel manifold.

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33

MOCHIZUKI, RIUJI. "STOCHASTIC CALCULUS AND COVARIANT AND ROTATION-INVARIANT LANGEVIN EQUATION FOR GRAVITY". Modern Physics Letters A 05, nr 28 (10.11.1990): 2335–42. http://dx.doi.org/10.1142/s0217732390002687.

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We investigate the relations among the Langevin equation, the Fokker-Planck equation, and the stochastic action, both in the sense of Ito and of Stratonovich. In the latter case we suggest a somewhat modified Langevin equation which is covariant and rotation-invariant.

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34

Walczak, Andrzej. "Patient treatment prediction by continuous time random walk inside complex system". MATEC Web of Conferences 210 (2018): 02006. http://dx.doi.org/10.1051/matecconf/201821002006.

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Stochastic resonance model for medical patient condition is proposed. Approach has been generalized by means of fractional Fokker-Planck equation and subdiffusion processes. Nonadditive entropy method has been used to achieve nonlinear fractional Fokker-Planck equation. We proved that duration of an unchanged patient situation can be estimated and fulfills rules for “fat tail” probability distribution. We also proved that probability of patient staying in an unchanged condition behaves the same. Formal rules were built on concept of similarity between real patient condition and potential well model. Such approach is new and allows new results as alternative for discrete models of prediction. Obtained results get probability for patient health parameter behavior in really detailed way.

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Jensen, Henrik Jeldtoft. "Emergence of network structure in models of collective evolution and evolutionary dynamics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, nr 2096 (10.03.2008): 2207–17. http://dx.doi.org/10.1098/rspa.2008.0032.

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We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The properties of the degree distribution in the stationary state is analysed by use of the Fokker–Planck equation. For a broad range of parameters, exponential degree distributions are observed. The mechanism responsible for this behaviour is illuminated by use of a simple mean field equation and reproduced by the Fokker–Planck equation. The latter is treated exactly, except for an approximate treatment of the degree–degree correlations. In the limit of 0 mutations, the degree distribution becomes a power law with exponent 1.

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36

Aljethi, Reem Abdullah, i Adem Kılıçman. "Derivation of the Fractional Fokker–Planck Equation for Stable Lévy with Financial Applications". Mathematics 11, nr 5 (22.02.2023): 1102. http://dx.doi.org/10.3390/math11051102.

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This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical solution is chosen to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. We model market data using a stable distribution to demonstrate the relationships between the tails and the new fractional Fokker–Planck model, as well as develop an R code that can be used to draw figures from real data.

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Haba, Z. "Statistical Physics of the Inflaton Decaying in an Inhomogeneous Random Environment". Advances in High Energy Physics 2018 (9.07.2018): 1–9. http://dx.doi.org/10.1155/2018/7204952.

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We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton probability distribution is derived. The relative entropy (free energy) of the stochastic wave is defined. The second law of thermodynamics for the diffusive system is obtained. Gaussian probability distributions are studied in detail.

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Millonas, Mark M., i Linda E. Reichl. "Stochastic chaos in a class or Fokker-Planck equations". Physical Review Letters 68, nr 21 (25.05.1992): 3125–28. http://dx.doi.org/10.1103/physrevlett.68.3125.

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Reichl, L. E., Zhong-Ying Chen i M. Millonas. "Stochastic manifestation of chaos in a Fokker-Planck equation". Physical Review Letters 63, nr 19 (6.11.1989): 2013–16. http://dx.doi.org/10.1103/physrevlett.63.2013.

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Grigolini, P., L. A. Lugiato, R. Mannella, P. V. E. McClintock, M. Merri i M. Pernigo. "Fokker-Planck description of stochastic processes with colored noise". Physical Review A 38, nr 4 (1.08.1988): 1966–78. http://dx.doi.org/10.1103/physreva.38.1966.

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Mais, H., i M. P. Zorzano. "Stochastic dynamics and Fokker-Planck equation in accelerator physics". Il Nuovo Cimento A 112, nr 5 (maj 1999): 467–74. http://dx.doi.org/10.1007/bf03035859.

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Annunziato, M., i A. Borzì. "A Fokker–Planck control framework for multidimensional stochastic processes". Journal of Computational and Applied Mathematics 237, nr 1 (styczeń 2013): 487–507. http://dx.doi.org/10.1016/j.cam.2012.06.019.

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Kumar, Mohit, Norbert Stoll i Regina Stoll. "Stationary Fuzzy Fokker–Planck Learning and Stochastic Fuzzy Filtering". IEEE Transactions on Fuzzy Systems 19, nr 5 (październik 2011): 873–89. http://dx.doi.org/10.1109/tfuzz.2011.2148724.

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Giona, Massimiliano, Antonio Brasiello i Alessandra Adrover. "Space-Time Inversion of Stochastic Dynamics". Symmetry 12, nr 5 (20.05.2020): 839. http://dx.doi.org/10.3390/sym12050839.

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This article introduces the concept of space-time inversion of stochastic Langevin equations as a way of transforming the parametrization of the dynamics from time to a monotonically varying spatial coordinate. A typical physical problem in which this approach can be fruitfully used is the analysis of solute dispersion in long straight tubes (Taylor-Aris dispersion), where the time-parametrization of the dynamics is recast in that of the axial coordinate. This allows the connection between the analysis of the forward (in time) evolution of the process and that of its exit-time statistics. The derivation of the Fokker-Planck equation for the inverted dynamics requires attention: it can be deduced using a mollified approach of the Wiener perturbations “a-la Wong-Zakai” by considering a sequence of almost everywhere smooth stochastic processes (in the present case, Poisson-Kac processes), converging to the Wiener processes in some limit (the Kac limit). The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. Several examples ranging from stochastic thermodynamics and fractal-time models are also analyzed.

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NAKAZAWA, NAOHITO. "ON FIELD THEORIES OF LOOPS". Modern Physics Letters A 10, nr 29 (21.09.1995): 2175–84. http://dx.doi.org/10.1142/s0217732395002337.

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We apply stochastic quantization method to real symmetric matrix models for the second quantization of nonorientable loops in both discretized and continuum levels. The stochastic process defined by the Langevin equation in loop space describes the time evolution of the nonorientable loops defined on nonorientable 2-D surfaces. The corresponding Fokker-Planck Hamiltonian deduces a nonorientable string field theory at the continuum limit.

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MOCHIZUKI, RIUJI. "THE STOCHASTIC QUANTIZATION METHOD IN PHASE SPACE AND A NEW GAUGE FIXING PROCEDURE". Modern Physics Letters A 09, nr 30 (28.09.1994): 2803–15. http://dx.doi.org/10.1142/s0217732394002641.

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We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are automatically selected and introduced by imposing stochastic consistency conditions upon the first class constraints. Then the equilibrium solution of the Fokker–Planck equation is identical to the corresponding path-integral distribution.

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Boulanger, Nicolas, Fabien Buisseret, Victor Dehouck, Frédéric Dierick i Olivier White. "Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion during Long-Range Walking". Physics 5, nr 1 (5.02.2023): 168–78. http://dx.doi.org/10.3390/physics5010013.

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When a Hamiltonian system undergoes a stochastic, time-dependent anharmonic perturbation, the values of its adiabatic invariants as a function of time follow a distribution whose shape obeys a Fokker–Planck equation. The effective dynamics of the body’s centre-of-mass during human walking is expected to represent such a stochastically perturbed dynamical system. By studying, in phase space, the vertical motion of the body’s centre-of-mass of 25 healthy participants walking for 10 min at spontaneous speed, we show that the distribution of the adiabatic invariant is compatible with the solution of a Fokker–Planck equation with a constant diffusion coefficient. The latter distribution appears to be a promising new tool for studying the long-range kinematic variability of walking.

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Lee, John. "Random Vibration of Thermally Buckled Plates: II Nonzero Temperature Gradient Across the Plate Thickness". Applied Mechanics Reviews 50, nr 11S (1.11.1997): S105—S116. http://dx.doi.org/10.1115/1.3101821.

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As a theoretical tool, we use the single-mode Fokker-Planck distribution for an isotropic plate to describe the random vibration of thermally buckled composite plates. The Fokker-Plank distribution becomes singular as uniform plate temperature far exceeds, say, 20 times the critical buckling temperature. Then the asymptotic high-temperature moments depend only on the snap-through displacement, testifying that stochastic dynamics has degenerated into a static snap-through problem in the limit of high plate temperature and large temperature gradient across the plate thickness. Otherwise, it is nonsingular and bimodal for low and moderate plate temperatures. From the nonsingular Fokker-Planck distribution, we have deduced peak scaling by the standard deviation of displacement distribution and derived a functional form for strain distribution by using the quadratic relation between strain and displacement. They have been validated by the displacement histograms of numerical simulations and the strain histograms of thermally buckled plate experiments.

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Papież, Lech S., i George A. Sandison. "A diffusion model with loss of particles". Advances in Applied Probability 22, nr 3 (wrzesień 1990): 533–47. http://dx.doi.org/10.2307/1427456.

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The dynamical behaviour of particles which undergo diffusion with annihilation is modelled by a parabolic (Fokker–Planck) equation. Fundamental, closed-form solutions of this equation, identified with transition densities of the underlying stochastic process, are calculated by utilizing specific methods of probability measures on functional spaces and evolution semigroups.

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Papież, Lech S., i George A. Sandison. "A diffusion model with loss of particles". Advances in Applied Probability 22, nr 03 (wrzesień 1990): 533–47. http://dx.doi.org/10.1017/s0001867800019868.

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The dynamical behaviour of particles which undergo diffusion with annihilation is modelled by a parabolic (Fokker–Planck) equation. Fundamental, closed-form solutions of this equation, identified with transition densities of the underlying stochastic process, are calculated by utilizing specific methods of probability measures on functional spaces and evolution semigroups.

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