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Littérature scientifique sur le sujet « G-stochastic integral »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 10 mars 2023

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Articles de revues sur le sujet "G-stochastic integral"

HERNÁNDEZ, JORGE ELIECER. "ON (m, h1, h2)-G-CONVEX DOMINATED STOCHASTIC PROCESSES." Kragujevac Journal of Mathematics 46, no. 2 (2022): 215–27. http://dx.doi.org/10.46793/kgjmat2202.215h.

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In this paper is introduced the concept of (m, h1, h2)-convexity for stochastic processes dominated by other stochastic processes with the same property, some mean square integral Hermite-Hadamard type inequalities for this kind of generalized convexity are established and from the founded results, other mean square integral inequalities for the classical convex, s-convex in the first and second sense, P-convex and MT-convex stochastic processes are deduced.

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Aoyama, Takahiro, та Makoto Maejima. "Characterizations of subclasses of type G distributions on $ℝ^d$ by stochastic integral representations". Bernoulli 13, № 1 (2007): 148–60. http://dx.doi.org/10.3150/07-bej5136.

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Cuong, Dang Kien, Duong Ton Dam, Duong Ton Thai Duong, and Du Thuan Ngo. "Solutions to the jump-diffusion linear stochastic differential equations." Science and Technology Development Journal - Natural Sciences 3, no. 2 (2019): 115–19. http://dx.doi.org/10.32508/stdjns.v3i2.663.

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The jump-diffusion stochastic process is one of the most common forms in reality (such as wave propagation, noise propagation, turbulent flow, etc.), and researchers often refer to them in models of random processes such as Wiener process, Levy process, Ito-Hermite process, in research of G. D. Nunno, B. Oksendal, F. B. Hanson, etc. In our research, we have reviewed and solved three problems: (1) Jump-diffusion process (also known as the Ito-Levy process); (2) Solve the differential equation jump-diffusion random linear, in the case of one-dimensional; (3) Calculate the Wiener-Ito integral to the random Ito-Hermite process. The main method for dealing with the problems in our presentation is the Ito random-integrable mathematical operations for the continuous random process associated with the arbitrary differential jump by the Poisson random measure. This study aims to analyse the basic properties of jump-diffusion process that are solutions to the jump-diffusion linear stochastic differential equations: dX(t) = [a (t)X (t􀀀)+A(t)]dt + [b (t)X (t􀀀 ∫ )+B(t)]dW (t) + R0 [g (t; z)X (t􀀀)+G(t; z)] ¯N (dt;dz) with a set of stochastic continuous functions fa;b ;g ;A;B;Gg and assuming that the compensated Poisson process ¯N (t; z) is independent of the Wiener process W(t). Derived from the Ito-Hermite formulas for the Ito-Hermite process and for the Ito-Levy process class we presented the results for the differential and multiple stochastic integration for the Ito- Hermite process. We also provided a separation method to solve jump-diffusion linear differential equations.

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Ma, Li, and Yujing Li. "Stability Analysis of Stochastic Differential Equation Driven by G-Brownian Motion under Non-Lipschitz Condition." Mathematical Problems in Engineering 2022 (September 1, 2022): 1–16. http://dx.doi.org/10.1155/2022/7592535.

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This paper is devoted to studying the p-th moment exponential stability for a class of stochastic differential equation (SDE) driven by G-Brownian motion under non-Lipschitz condition. The delays considered in this paper are time-varying delays τ i t 1 ≤ i ≤ 3 . Since the coefficients are non-Lipschitz, the normal enlargement on the coefficients is not available and the Gronwall inequality is not suitable in this case. By Bihari inequality and Itô integral formula, it is pointed out that there exists a constant τ ∗ such that the p-th moment exponential stability holds if the time-varying delays are smaller than τ ∗ .

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Noeiaghdam, Samad, and Mohammad Ali Fariborzi Araghi. "A Novel Algorithm to Evaluate Definite Integrals by the Gauss-Legendre Integration Rule Based on the Stochastic Arithmetic: Application in the Model of Osmosis System." Mathematical Modelling of Engineering Problems 7, no. 4 (2020): 577–86. http://dx.doi.org/10.18280/mmep.070410.

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Finding the optimal iteration of Gaussian quadrature rule is one of the important problems in the computational methods. In this study, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library to find the optimal iteration and optimal approximation of the Gauss-Legendre integration rule (G-LIR). A theorem is proved to show the validation of the presented method based on the concept of the common significant digits. Applying this method, an improper integral in the solution of the model of the osmosis system is evaluated and the optimal results are obtained. Moreover, the accuracy of method is demonstrated by evaluating other definite integrals. The results of examples illustrate the importance of using the stochastic arithmetic in discrete case in comparison with the common computer arithmetic.

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Zhang, Yunlong, Weizhi Xu, Dongsheng Du, and Shuguang Wang. "Stochastic Optimization of Dissipation Structures Based on Lyapunov Differential Equations and the Full Stress Design Method." Buildings 13, no. 3 (2023): 665. http://dx.doi.org/10.3390/buildings13030665.

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This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for the damping system under the excitation of a nonstationary stochastic process using two types of modulation functions: g(t)=1 and g(t)=t. Finally, the optimal damping arrangement is achieved using this method with a six-layer non-eccentric planar frame. In addition, the optimization results of this study are verified with those in the literature using time-history analysis, which verifies the feasibility and effectiveness of the proposed method. This study provides a method for the optimal configuration of dampers for seismic response of structures, which is beneficial for engineering applications and the protection of seismic structures.

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Yukich, J. E. "The convolution metric dg." Mathematical Proceedings of the Cambridge Philosophical Society 98, no. 3 (1985): 533–40. http://dx.doi.org/10.1017/s0305004100063738.

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SummaryWe introduce and study a new metric on denned bywhere is the space of probability measures on ℝk and where g: ℝk→ is a probability density satisfying certain mild conditions. The metric dg, relatively easy to compute, is shown to have useful and interesting properties not enjoyed by some other metrics on . In particular, letting pn denote the nth empirical measure for P, it is shown that under appropriate conditions satisfies a compact law of the iterated logarithm, converges in probability to the supremum of a Gaussian process, and has a useful stochastic integral representation.

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Bai, Xue-peng, and Yi-qing Lin. "On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients." Acta Mathematicae Applicatae Sinica, English Series 30, no. 3 (2014): 589–610. http://dx.doi.org/10.1007/s10255-014-0405-9.

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Cortés, Juan Carlos, and Marc Jornet. "Lp-Solution to the Random Linear Delay Differential Equation with a Stochastic Forcing Term." Mathematics 8, no. 6 (2020): 1013. http://dx.doi.org/10.3390/math8061013.

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This paper aims at extending a previous contribution dealing with the random autonomous-homogeneous linear differential equation with discrete delay τ > 0 , by adding a random forcing term f ( t ) that varies with time: x ′ ( t ) = a x ( t ) + b x ( t − τ ) + f ( t ) , t ≥ 0 , with initial condition x ( t ) = g ( t ) , − τ ≤ t ≤ 0 . The coefficients a and b are assumed to be random variables, while the forcing term f ( t ) and the initial condition g ( t ) are stochastic processes on their respective time domains. The equation is regarded in the Lebesgue space L p of random variables with finite p-th moment. The deterministic solution constructed with the method of steps and the method of variation of constants, which involves the delayed exponential function, is proved to be an L p -solution, under certain assumptions on the random data. This proof requires the extension of the deterministic Leibniz’s integral rule for differentiation to the random scenario. Finally, we also prove that, when the delay τ tends to 0, the random delay equation tends in L p to a random equation with no delay. Numerical experiments illustrate how our methodology permits determining the main statistics of the solution process, thereby allowing for uncertainty quantification.

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KONDRATIEV, YURI G., and EUGENE W. LYTVYNOV. "OPERATORS OF GAMMA WHITE NOISE CALCULUS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 03 (2000): 303–35. http://dx.doi.org/10.1142/s0219025700000236.

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The paper is devoted to the study of Gamma white noise analysis. We define an extended Fock space ℱ ext (ℋ) over ℋ= L2(ℝd, dσ) and show how to include the usual Fock space ℱ(ℋ) in it as a subspace. We introduce in ℱ ext (ℋ) operators a(ξ)=∫ℝddxξ(x)a(x), ξ∈ S, with [Formula: see text], where [Formula: see text] and ∂x are the creation and annihilation operators at x. We show that (a(ξ))ξ∈S is a family of commuting self-adjoint operators in ℱ ext (ℋ) and construct the Fourier transform in generalized joint eigenvectors of this family. This transform is a unitary I between ℱ ext (ℋ) and the L2-space L2(S', dμ G ), where μ G is the measure of Gamma white noise with intensity σ. The image of a(ξ) under I is the operator of multiplication by <·,ξ>, so that a(ξ)'s are Gamma field operators. The Fock structure of the Gamma space determined by I coincides with that discovered in Ref. 22. We note that I extends in a natural way the multiple stochastic integral (chaos) decomposition of the "chaotic" subspace of the Gamma space. Next, we introduce and study spaces of test and generalized functions of Gamma white noise and derive explicit formulas for the action of the creation, neutral, and Gamma annihilation operators on these spaces.

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Thèses sur le sujet "G-stochastic integral"

IBRAGIMOV, ANTON. "G - Expectations in infinite dimensional spaces and related PDES." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/44738.

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In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.

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