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Maple for Stochastic Differential Equations [PDF]
, 2001 This paper introduces the MAPLE software package stochastic consisting of MAPLE routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines.
Grüne, Lars +2 more
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Strong Law of Large Numbers for Solutions of Non-Autonomous Stochastic Differential Equations
Наукові вісті Національного технічного університету України "Київський політехнічний інститут", 2017 Background. Asymptotic behavior at infinity of non-autonomous stochastic differential equation solutions is studied in the paper. Objective. The aim of the work is to find sufficient conditions for the strong law of large numbers for a random process ...
Oleg I. Klesov +2 more
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Efficient Memristive Stochastic Differential Equation Solver
Advanced Intelligent Systems, 2023 Herein, an efficient numerical solver for stochastic differential equations based on memristors is presented. The solver utilizes the stochastic switching effect in memristive devices to simulate the generation of a Brownian path and employs iterative ...
Xuening Dong +4 more
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Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise
Nonlinear Analysis, 2021 The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for
Gregory Amali Paul Rose +2 more
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Stochastic model of innovation diffusion that takes into account the changes in the total market volume [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2022 The article proposes a stochastic mathematical model of the diffusion of consumer innovations, which takes into account changes over time in the total number of potential buyers of an innovative product.
Parphenova, Alena Yu., Saraev, Leonid A.
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L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension [PDF]
Arab Journal of Mathematical SciencesPurpose – The main motivation of this paper is to present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.
Hani Abidi +3 more
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Stochastic Differential Equations in a Differentiable Manifold [PDF]
Nagoya Mathematical Journal, 1950 The theory of stochastic differential equations in a differentiate manifold has been established by many authors from different view-points, especially by R Lévy [2], F. Perrin [1], A. Kolmogoroff [1] [2] and K. Yosida [1] [2]. It is the purpose of the present paper to discuss it by making use of stochastic integrals.
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Harmonic analysis of stochastic equations and backward stochastic differential equations [PDF]
Probability Theory and Related Fields, 2008 The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $\cR^p$ ($p\in [1, \infty)$) and backward stochastic differential equations (BSDEs) in $\cR^p\times \cH^p$ ($p\in (1, \infty)$) and in $\cR^\infty\times \bar{\cH^\infty}^{BMO}$, with the coefficients being allowed to be unbounded.
Delbaen, Freddy, Tang, Shanjian
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A kind of non-zero sum mixed differential game of backward stochastic differential equation
Advances in Difference Equations, 2020 This paper is concerned with a non-zero sum mixed differential game problem described by a backward stochastic differential equation. Here the term “mixed” means that this game problem contains a deterministic control v1 $v_{1}$ of Player 1 and a random ...
Huanjun Zhang
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Partial Differential Equations in Applied Mathematics, 2022 Backward stochastic differential equation solver was first introduced by Han et al in 2017. A semilinear parabolic partial differential equation is converted into a stochastic differential equation, and then solved by the backward stochastic differential
Evan Davis +4 more
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