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Journal articles on the topic 'La probabilité de diffusion'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Grignon, Michel, Byron G. Spencer, and Li Wang. "Is There an Age Pattern in the Treatment of AMI? Evidence from Ontario." Canadian Journal on Aging / La Revue canadienne du vieillissement 29, no. 3 (August 24, 2010): 317–32. http://dx.doi.org/10.1017/s0714980810000383.

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RÉSUMÉDans cet article nous analysons la probabilité pour un patient hospitalisé pour infarctus du myocarde de recevoir des traitements chirurgicaux, puis nous mesurons les changements dans le temps de cette probabilité et cherchons à savoir si l’âge du patient joue sur la probabilité. Nos estimations, fondées sur des données administratives incluant tous les séjours dans les hôpitaux de soins aigus de l’Ontario pour certaines années entre 1995 et 2005, font état d’un profil par âge marqué et stable dans le temps dans la diffusion de la technologie médicale. Nos résultats montrent que ceci est robuste à l’inclusion de contrôles pour la plus forte fréquence de co-morbidités chez les patients âgés ainsi que pour les effets de pratiques propres aux hôpitaux.

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2

Pardo, A., and G. Sapiro. "Vector probability diffusion." IEEE Signal Processing Letters 8, no. 4 (April 2001): 106–9. http://dx.doi.org/10.1109/97.911471.

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3

Tupper, P. F., and Xin Yang. "A paradox of state-dependent diffusion and how to resolve it." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (September 5, 2012): 3864–81. http://dx.doi.org/10.1098/rspa.2012.0259.

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Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region, the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal proportions of time in the two regions in the long term? Statistical mechanics would suggest yes, since the number of accessible states in each region is presumably the same. However, another line of reasoning suggests that the particle should spend less time in the region with faster diffusion, since it will exit that region more quickly. We demonstrate with a simple microscopic model system that both predictions are consistent with the information given. Thus, specifying the diffusion rate as a function of position is not enough to characterize the behaviour of a system, even assuming the absence of external forces. We propose an alternative framework for modelling diffusive dynamics in which both the diffusion rate and equilibrium probability density for the position of the particle are specified by the modeller. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and is suitable for discontinuous diffusion coefficients.

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4

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 4 (December 2010): 1147–71. http://dx.doi.org/10.1239/aap/1293113155.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

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5

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 04 (December 2010): 1147–71. http://dx.doi.org/10.1017/s0001867800004560.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

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6

Bouchard, Gérard, Jean Morissette, and Kevork Kouladjian. "La statistique agrégée des patronymes du Saguenay et de Charlevoix comme indicateurs de la structure de la population aux XIXe et XXe siècles." Articles 16, no. 1 (October 20, 2008): 67–98. http://dx.doi.org/10.7202/600608ar.

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RÉSUMÉ L’analyse de la statistique des patronymes du Saguenay et de Charlevoix depuis le XIXe siècle suggère que les populations de ces deux régions sont extrêmement similaires, l’une ayant été créée à partir de l’autre. S’agissant plus particulièrement du Saguenay, les structures du bassin patronymique y sont demeurées relativement stables entre 1842 et 1971. Les auteurs pensent que, à titre préliminaire, la statistique des noms de famille peut être un indicateur utile non seulement de la dynamique d’une population, mais aussi de l’ensemble de son bassin génétique. Elle semble cependant mal refléter la diffusion d’un gène en particulier : on ne trouve pas ici de corrélation entre le fait de porter tel nom et la probabilité de porter tel ou tel gène délétère.

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7

Pagnini, Gianni. "Subordination Formulae for Space-time Fractional Diffusion Processes via Mellin Convolution." International Journal of Mathematical Models and Methods in Applied Sciences 16 (March 12, 2022): 71–76. http://dx.doi.org/10.46300/9101.2022.16.13.

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Fundamental solutions of space-time fractional diffusion equations can be interpret as probability density functions. This fact creates a strong link with stochastic processes. Recasting probability density functions in terms of subordination laws has emerged to be important to built up stochastic processes. In particular, for diffusion processes, subordination can be understood as a diffusive process in space, which is called parent process, that depends on a parameter which is also random and depends on time, which is called directing process. Stochastic processes related to fractional diffusion are self-similar processes. The integral representation of the resulting probability density function for self-similar stochastic processes can be related to the convolution integral within the Mellin transform theory. Here, subordination formulae for space-time fractional diffusion are provided. In particular, a noteworthy new formula is derived in the diffusive symmetric case that is spatially driven by the Gaussian density. Future developments of the research on the basis of this new subordination law are discussed.

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8

Abundo, Mario. "First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes." Open Systems & Information Dynamics 16, no. 04 (December 2009): 325–50. http://dx.doi.org/10.1142/s1230161209000256.

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For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported.

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9

Bustreel, Anne, Frédérique Cornuau, and Martine Pernod-Lemattre. "Concilier vie familiale et vie professionnelle en France : les disparités d’horaires de travail." Autres articles 67, no. 4 (December 5, 2012): 681–702. http://dx.doi.org/10.7202/1013200ar.

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Résumé La France se caractérise aujourd’hui par une forte proportion de salariés ayant des contraintes familiales et par un nombre élevé d’entreprises qui flexibilisent la durée et les horaires de travail : comment la diffusion de ces nouvelles contraintes temporelles affectent-elles les femmes, et plus particulièrement les mères ? Une typologie des conditions temporelles d’emploi des salariés français intégrant la durée du travail, la souplesse horaire dont bénéficie le salarié et la « localisation » de son temps de travail, construite à partir de l’enquête « Familles et employeurs » (Ined-Insee, 2004-2005), fait apparaître une surreprésentation des femmes dans les emplois les plus souples, mais aussi les plus contraignants temporellement, alors que l’effet de la présence d’enfant semble assez mineur. Trois hypothèses sont testées pour expliquer les conditions temporelles d’emploi : la préférence des salariés pour des horaires de travail commodes, les caractéristiques productives des emplois et le rapport de force salarié-employeur. Les résultats montrent que le fait d’avoir de jeunes enfants n’est pas corrélé aux conditions temporelles d’emploi. Être une femme accroît la probabilité d’avoir des horaires hyper-souples (plutôt que standards contraints) et diminue la probabilité d’avoir des horaires longs souples et non standards contraints. L’hypothèse d’une sélection en fonction des préférences n’est pas confirmée par l’analyse alors que les exigences productives des emplois et des employeurs ainsi que le pouvoir de négociation des salariés exercent des effets significatifs et expliquent la surreprésentation des femmes dans les horaires fragmentés contraints.

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10

Shimizu, Akinobu. "A measure valued diffusion process describing an n locus model incorporating gene conversion." Nagoya Mathematical Journal 119 (September 1990): 81–92. http://dx.doi.org/10.1017/s0027763000003123.

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Probability measure valued diffusion processes have been discussed by many authors, in connection with population genetics. Most papers studying probability measure valued diffusions are mainly concerned with the ones describing single locus models. In this paper, we will discuss a measure valued diffusion describing an n locus model. Random sampling, mutation and gene conversion, a kind of interaction between loci, which was introduced and investigated by T. Ohta in [5], [6], will be taken into consideration.

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11

ZENG, QIUHUA, and HOUQIANG LI. "DIFFUSION EQUATION FOR DISORDERED FRACTAL MEDIA." Fractals 08, no. 01 (March 2000): 117–21. http://dx.doi.org/10.1142/s0218348x00000123.

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The movement of the fractal Brownian particle in isotropic and homogeneous two-dimensional assembling fractal spaces is studied by the standard diffusion equation on fractals, and we find that particle movement belongs to the anomalous diffusion. At the same time, by discussing the defectiveness of earlier proposed equations, a general form of analytic fractional diffusion equation is proposed for description of probability density of particles diffusing on fractal geometry at fractal time, and the solution connects with the ordinary solutions in the normal space time limit.

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12

ROY, S. D. D., and K. RAMACHANDRAN. "REFINED SIMULATION FOR THE DIFFUSION IN Sivia CHANDRASEKHAR HOPPING." International Journal of Modern Physics C 13, no. 07 (September 2002): 881–92. http://dx.doi.org/10.1142/s0129183102004583.

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The method employed by Chandrasekhar for the astronomical bodies is brought down here to study the diffusion in Silicon. A continuous position probability density for the diffusing particle, ω(r, t) representing the position of the diffusing particle at any time t, is used in the evaluation of the diffusion constant. The results agree reasonably well with the available experimental and theoretically reported values. The existence of "traps" in the semiconducting systems has been clearly brought out by this simulation technique.

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13

Yan, Fuhan, Zhaofeng Li, and Yichuan Jiang. "Controllable uncertain opinion diffusion under confidence bound and unpredicted diffusion probability." Physica A: Statistical Mechanics and its Applications 449 (May 2016): 85–100. http://dx.doi.org/10.1016/j.physa.2015.12.110.

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14

Kloeden, P. E., E. Platen, H. Schurz, and M. Sørensen. "On effects of discretization on estimators of drift parameters for diffusion processes." Journal of Applied Probability 33, no. 4 (December 1996): 1061–76. http://dx.doi.org/10.2307/3214986.

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In this paper statistical properties of estimators of drift parameters for diffusion processes are studied by modern numerical methods for stochastic differential equations. This is a particularly useful method for discrete time samples, where estimators can be constructed by making discrete time approximations to the stochastic integrals appearing in the maximum likelihood estimators for continuously observed diffusions. A review is given of the necessary theory for parameter estimation for diffusion processes and for simulation of diffusion processes. Three examples are studied.

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15

Drew, Donald A. "Probability and repeatibility: One particle diffusion." Nuclear Engineering and Design 235, no. 10-12 (May 2005): 1117–28. http://dx.doi.org/10.1016/j.nucengdes.2005.02.009.

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16

Hinkel, Julia, and Reinhard Mahnke. "Outflow Probability for Drift–Diffusion Dynamics." International Journal of Theoretical Physics 46, no. 6 (January 3, 2007): 1542–61. http://dx.doi.org/10.1007/s10773-006-9291-0.

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17

Donchev, Doncho S. "Exit probability levels of diffusion processes." Proceedings of the American Mathematical Society 145, no. 5 (January 27, 2017): 2241–53. http://dx.doi.org/10.1090/proc/13392.

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18

FORMAN, JULIE LYNG, and MICHAEL SØRENSEN. "The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes." Scandinavian Journal of Statistics 35, no. 3 (September 2008): 438–65. http://dx.doi.org/10.1111/j.1467-9469.2007.00592.x.

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19

Rhodes, Rémi. "Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 45, no. 4 (November 2009): 981–1001. http://dx.doi.org/10.1214/08-aihp190.

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20

Kelly, Leah, Eckhard Platen, and Michael Sørensen. "Estimation for discretely observed diffusions using transform functions." Journal of Applied Probability 41, A (2004): 99–118. http://dx.doi.org/10.1239/jap/1082552193.

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This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

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21

Rabinovich, Savely, and Noam Agmon. "The slow diffusion limit for the survival probability in reactive diffusion equations." Chemical Physics 148, no. 1 (November 1990): 11–19. http://dx.doi.org/10.1016/0301-0104(90)89002-8.

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22

Sun, Ling, Yun Liu, Qing-An Zeng, and Fei Xiong. "A novel rumor diffusion model considering the effect of truth in online social media." International Journal of Modern Physics C 26, no. 07 (April 30, 2015): 1550080. http://dx.doi.org/10.1142/s0129183115500801.

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In this paper, we propose a model to investigate how truth affects rumor diffusion in online social media. Our model reveals a relation between rumor and truth — namely, when a rumor is diffusing, the truth about the rumor also diffuses with it. Two patterns of the agents used to identify rumor, self-identification and passive learning are taken into account. Combining theoretical proof and simulation analysis, we find that the threshold value of rumor diffusion is negatively correlated to the connectivity between nodes in the network and the probability β of agents knowing truth. Increasing β can reduce the maximum density of the rumor spreaders and slow down the generation speed of new rumor spreaders. On the other hand, we conclude that the best rumor diffusion strategy must balance the probability of forwarding rumor and the probability of agents losing interest in the rumor. High spread rate λ of rumor would lead to a surge in truth dissemination which will greatly limit the diffusion of rumor. Furthermore, in the case of unknown λ, increasing β can effectively reduce the maximum proportion of agents who do not know the truth, but cannot narrow the rumor diffusion range in a certain interval of β.

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23

Mano, Shuhei. "A Measure-on-Graph-Valued Diffusion: A Particle System with Collisions and Its Applications." Mathematics 10, no. 21 (November 2, 2022): 4081. http://dx.doi.org/10.3390/math10214081.

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A diffusion-taking value in probability-measures on a graph with vertex set V, ∑i∈Vxiδi is studied. The masses on each vertex satisfy the stochastic differential equation of the form dxi=∑j∈N(i)xixjdBij on the simplex, where {Bij} are independent standard Brownian motions with skew symmetry, and N(i) is the neighbour of the vertex i. A dual Markov chain on integer partitions to the Markov semigroup associated with the diffusion is used to show that the support of an extremal stationary state of the adjoint semigroup is an independent set of the graph. We also investigate the diffusion with a linear drift, which gives a killing of the dual Markov chain on a finite integer lattice. The Markov chain is used to study the unique stationary state of the diffusion, which generalizes the Dirichlet distribution. Two applications of the diffusions are discussed: analysis of an algorithm to find an independent set of a graph, and a Bayesian graph selection based on computation of probability of a sample by using coupling from the past.

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24

Nagai, Tetsuro, Akira Yoshimori, and Susumu Okazaki. "Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154506. http://dx.doi.org/10.1063/5.0086949.

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A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.

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25

Grebenkov, Denis S. "An encounter-based approach for restricted diffusion with a gradient drift." Journal of Physics A: Mathematical and Theoretical 55, no. 4 (January 5, 2022): 045203. http://dx.doi.org/10.1088/1751-8121/ac411a.

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Abstract We develop an encounter-based approach for describing restricted diffusion with a gradient drift toward a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive a spectral decomposition for the full propagator, i.e. the joint probability density function for the particle position and its boundary local time. This is the central quantity that determines various characteristics of diffusion-influenced reactions such as conventional propagators, survival probability, first-passage time distribution, boundary local time distribution, and reaction rate. As an illustration, we investigate the impact of a constant drift onto the boundary local time for restricted diffusion on an interval. More generally, this approach accesses how external forces may influence the statistics of encounters of a diffusing particle with the reactive boundary.

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26

A. F. dos Santos, Maike. "Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels." Fractal and Fractional 2, no. 3 (July 29, 2018): 20. http://dx.doi.org/10.3390/fractalfract2030020.

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The investigation of diffusive process in nature presents a complexity associated withmemory effects. Thereby, it is necessary new mathematical models to involve memory conceptin diffusion. In the following, I approach the continuous time random walks in the context ofgeneralised diffusion equations. To do this, I investigate the diffusion equation with exponential andMittag–Leffler memory-kernels in the context of Caputo–Fabrizio and Atangana–Baleanu fractionaloperators on Caputo sense. Thus, exact expressions for the probability distributions are obtained,in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class ofdiffusive behaviour. Moreover, I propose a generalised model to describe the random walk processwith resetting on memory kernel context.

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27

Wu, Minnie M., Elizabeth D. Covington, and Richard S. Lewis. "Single-molecule analysis of diffusion and trapping of STIM1 and Orai1 at endoplasmic reticulum–plasma membrane junctions." Molecular Biology of the Cell 25, no. 22 (November 5, 2014): 3672–85. http://dx.doi.org/10.1091/mbc.e14-06-1107.

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Following endoplasmic reticulum (ER) Ca2+ depletion, STIM1 and Orai1 complexes assemble autonomously at ER–plasma membrane (PM) junctions to trigger store-operated Ca2+ influx. One hypothesis to explain this process is a diffusion trap in which activated STIM1 diffusing in the ER becomes trapped at junctions through interactions with the PM, and STIM1 then traps Orai1 in the PM through binding of its calcium release-activated calcium activation domain. We tested this model by analyzing STIM1 and Orai1 diffusion using single-particle tracking, photoactivation of protein ensembles, and Monte Carlo simulations. In resting cells, STIM1 diffusion is Brownian, while Orai1 is slightly subdiffusive. After store depletion, both proteins slow to the same speeds, consistent with complex formation, and are confined to a corral similar in size to ER–PM junctions. While the escape probability at high STIM:Orai expression ratios is <1%, it is significantly increased by reducing the affinity of STIM1 for Orai1 or by expressing the two proteins at comparable levels. Our results provide direct evidence that STIM-Orai complexes are trapped by their physical connections across the junctional gap, but also reveal that the complexes are surprisingly dynamic, suggesting that readily reversible binding reactions generate free STIM1 and Orai1, which engage in constant diffusional exchange with extrajunctional pools.

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28

Fuentes, Miguel. "Non-Linear Diffusion and Power Law Properties of Heterogeneous Systems: Application to Financial Time Series." Entropy 20, no. 9 (August 30, 2018): 649. http://dx.doi.org/10.3390/e20090649.

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In this work, we show that it is possible to obtain important ubiquitous physical characteristics when an aggregation of many systems is taken into account. We discuss the possibility of obtaining not only an anomalous diffusion process, but also a Non-Linear diffusion equation, that leads to a probability distribution, when using a set of non-Markovian processes. This probability distribution shows a power law behavior in the structure of its tails. It also reflects the anomalous transport characteristics of the ensemble of particles. This ubiquitous behavior, with a power law in the diffusive transport and the structure of the probability distribution, is related to a fast fluctuating phenomenon presented in the noise parameter. We discuss all the previous results using a financial time series example.

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29

Regenauer-Lieb, Klaus, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, et al. "Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory." Solid Earth 12, no. 4 (April 16, 2021): 869–83. http://dx.doi.org/10.5194/se-12-869-2021.

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Abstract. We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermo-hydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4×4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time–space relations entirely defined by the coefficients of the coupled THMC reaction–cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.

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Schwarzer, S., J. Lee, A. Bunde, S. Havlin, H. E. Roman, and H. E. Stanley. "Minimum growth probability of diffusion-limited aggregates." Physical Review Letters 65, no. 5 (July 30, 1990): 603–6. http://dx.doi.org/10.1103/physrevlett.65.603.

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31

Turkevich, Leonid A., and Harvey Scher. "Occupancy-Probability Scaling in Diffusion-Limited Aggregation." Physical Review Letters 55, no. 9 (August 26, 1985): 1026–29. http://dx.doi.org/10.1103/physrevlett.55.1026.

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32

Dana, Itzhack, and Vladislav E. Chernov. "Periodic orbits and chaotic-diffusion probability distributions." Physica A: Statistical Mechanics and its Applications 332 (February 2004): 219–29. http://dx.doi.org/10.1016/j.physa.2003.10.050.

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33

Rodríguez-Romo, Suemi, Vladimir Tchijov, Oscar Ibañez-Orozco, and Víctor M. Castaño. "Growth probability in bicolored diffusion limited aggregation." Physica A: Statistical Mechanics and its Applications 347 (March 2005): 301–13. http://dx.doi.org/10.1016/j.physa.2004.08.018.

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34

Adrian, Donald Dean, Vijay P. Singh, and Zhi-Qiang Deng. "Diffusion-Based Semi-Infinite Fourier Probability Distribution." Journal of Hydrologic Engineering 7, no. 2 (March 2002): 154–67. http://dx.doi.org/10.1061/(asce)1084-0699(2002)7:2(154).

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35

Zhang, Caiyun, Yuhang Hu, and Jian Liu. "Correlated continuous-time random walk with stochastic resetting." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 9 (September 1, 2022): 093205. http://dx.doi.org/10.1088/1742-5468/ac8c8e.

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Abstract It is known that the introduction of stochastic resetting in an uncorrelated random walk process can lead to the emergence of a stationary state, i.e. the diffusion evolves towards a saturation state, and a steady Laplace distribution is reached. In this paper, we turn to study the anomalous diffusion of the correlated continuous-time random walk considering stochastic resetting. Results reveal that it displays quite different diffusive behaviors from the uncorrelated one. For the weak correlation case, the stochastic resetting mechanism can slow down the diffusion. However, for the strong correlation case, we find that the stochastic resetting cannot compete with the space-time correlation, and the diffusion presents the same behaviors with the one without resetting. Meanwhile, a steady distribution is never reached.

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36

del-Castillo-Negrete, D. "Non-diffusive, non-local transport in fluids and plasmas." Nonlinear Processes in Geophysics 17, no. 6 (December 20, 2010): 795–807. http://dx.doi.org/10.5194/npg-17-795-2010.

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Abstract. A review of non-diffusive transport in fluids and plasmas is presented. In the fluid context, non-diffusive chaotic transport by Rossby waves in zonal flows is studied following a Lagrangian approach. In the plasma physics context the problem of interest is test particle transport in pressure-gradient-driven plasma turbulence. In both systems the probability density function (PDF) of particle displacements is strongly non-Gaussian and the statistical moments exhibit super-diffusive anomalous scaling. Fractional diffusion models are proposed and tested in the quantitative description of the non-diffusive Lagrangian statistics of the fluid and plasma problems. Also, fractional diffusion operators are used to construct non-local transport models exhibiting up-hill transport, multivalued flux-gradient relations, fast pulse propagation phenomena, and "tunneling" of perturbations across transport barriers.

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37

Feng, Shui, and Feng-Yu Wang. "A Class of Infinite-Dimensional Diffusion Processes with Connection to Population Genetics." Journal of Applied Probability 44, no. 4 (December 2007): 938–49. http://dx.doi.org/10.1239/jap/1197908815.

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Starting from a sequence of independent Wright-Fisher diffusion processes on [0, 1], we construct a class of reversible infinite-dimensional diffusion processes on Δ∞ := {x ∈ [0, 1]N: ∑i≥1xi = 1} with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence of the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space S. This provides a reasonable alternative to the Fleming-Viot process, which does not satisfy the log-Sobolev inequality when S is infinite as observed by Stannat (2000).

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38

García-Pareja, Celia, Henrik Hult, and Timo Koski. "Exact simulation of coupled Wright–Fisher diffusions." Advances in Applied Probability 53, no. 4 (November 22, 2021): 923–50. http://dx.doi.org/10.1017/apr.2021.9.

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AbstractIn this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

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39

Giorno, V., A. G. Nobile, and L. M. Ricciardi. "On some time-non-homogeneous diffusion approximations to queueing systems." Advances in Applied Probability 19, no. 4 (December 1987): 974–94. http://dx.doi.org/10.2307/1427111.

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Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

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40

Giorno, V., A. G. Nobile, and L. M. Ricciardi. "On some time-non-homogeneous diffusion approximations to queueing systems." Advances in Applied Probability 19, no. 04 (December 1987): 974–94. http://dx.doi.org/10.1017/s0001867800017523.

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Time-non-homogeneous diffusion approximations to single server–single queue–FCFS discipline systems are considered. Under various assumptions on the nature of the time-dependent functions appearing in the infinitesimal moments the transient and the regime behaviour of the approximating diffusions are analysed in some detail. Special attention is then given to the study of a diffusion approximation characterized by a linear drift and by a periodically time-varying infinitesimal variance. Unlike the behaviour of transition functions and moments, the p.d.f. of the busy period is seen to be unaffected by the presence of such periodicity.

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41

Borkar, Vivek S. "Controlled diffusion processes." Probability Surveys 2 (2005): 213–44. http://dx.doi.org/10.1214/154957805100000131.

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42

Fannjiang, Albert, and George Papanicolaou. "Diffusion in turbulence." Probability Theory and Related Fields 105, no. 3 (July 1, 1996): 279–334. http://dx.doi.org/10.1007/s004400050046.

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43

Fannjiang, Albert, and George Papanicolaou. "Diffusion in turbulence." Probability Theory and Related Fields 105, no. 3 (September 1996): 279–334. http://dx.doi.org/10.1007/bf01192211.

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44

Komorowski, Tomasz. "Diffusion approximation for the convection-diffusion equation with random drift." Probability Theory and Related Fields 121, no. 4 (December 2001): 525–50. http://dx.doi.org/10.1007/s004400100159.

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45

Silva, A. T., E. K. Lenzi, L. R. Evangelista, M. K. Lenzi, and L. R. da Silva. "Fractional nonlinear diffusion equation, solutions and anomalous diffusion." Physica A: Statistical Mechanics and its Applications 375, no. 1 (February 2007): 65–71. http://dx.doi.org/10.1016/j.physa.2006.09.001.

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46

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 2 (June 2005): 435–60. http://dx.doi.org/10.1239/aap/1118858633.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

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47

Bladt, Mogens, and Michael Sørensen. "Simple simulation of diffusion bridges with application to likelihood inference for diffusions." Bernoulli 20, no. 2 (May 2014): 645–75. http://dx.doi.org/10.3150/12-bej501.

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48

Feng, Shui, and Feng-Yu Wang. "A Class of Infinite-Dimensional Diffusion Processes with Connection to Population Genetics." Journal of Applied Probability 44, no. 04 (December 2007): 938–49. http://dx.doi.org/10.1017/s0021900200003648.

Full text

Abstract:

Starting from a sequence of independent Wright-Fisher diffusion processes on [0, 1], we construct a class of reversible infinite-dimensional diffusion processes on Δ∞ := { x ∈ [0, 1] N : ∑ i≥1 x i = 1} with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence of the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space S. This provides a reasonable alternative to the Fleming-Viot process, which does not satisfy the log-Sobolev inequality when S is infinite as observed by Stannat (2000).

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49

Gabrielli, Andrea, and Fabio Cecconi. "Diffusion, super-diffusion and coalescence from a single step." Journal of Statistical Mechanics: Theory and Experiment 2007, no. 10 (October 11, 2007): P10007. http://dx.doi.org/10.1088/1742-5468/2007/10/p10007.

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50

Boyarsky, Abraham, and Pawel Góra. "A description of stochastic systems using chaotic maps." Journal of Applied Mathematics and Stochastic Analysis 2004, no. 2 (January 1, 2004): 137–41. http://dx.doi.org/10.1155/s1048953304308026.

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Let ρ(x,t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τ1:t>0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x,t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose solution yields the family of chaotic maps whose density functions are precisely those of the diffusion.

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