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The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation [PDF]
Indiana University Mathematics Journal, 2020 One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+{\rm div}(D(x)b(u)u)=0, \ t\geq0, \ x\in\mathbb{R}^d,\qquad (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and $b$ the ...
Barbu, Viorel, Röckner, Michael
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Advances in Difference Equations, 2011 This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space.
N'Guérékata Gaston +2 more
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A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis [PDF]
Infectious Disease Modelling, 2017 Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used
Linda J.S. Allen
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The averaging principle for stochastic differential equations driven by a Wiener process revisited [PDF]
Comptes rendus. Mathematique, 2021 We consider a one-dimensional stochastic differential equation driven by a Wiener process, where the diffusion coefficient depends on an ergodic fast process.
Charles-Edouard Br'ehier
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Open Mathematics, 2021 The aim of this work is to study the asymptotic stability of the time-changed stochastic delay differential equations (SDDEs) with Markovian switching.
Zhang Xiaozhi +2 more
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Comptes rendus. Mathematique, 2021 This paper deals with a class of scalar backward stochastic differential equations (BSDEs) with L exp(μ0 √ 2log(1+L))-integrable terminal values for a critical parameter μ0 > 0.
H. O, Mun-chol Kim, Chol-Gyu Pak
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On copulas of self-similar Ito processes
Dependence Modeling, 2021 We characterize the cumulative distribution functions and copulas of two-dimensional self-similar Ito processes, with randomly correlated Wiener margins, as solutions of certain elliptic partial differential equations.
Jaworski Piotr, Krzywda Marcin
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A stochastic maximum principle for forward-backward stochastic control systems with quadratic generators and sample-wise constraints [PDF]
E S A I M: Control, Optimisation and Calculus of Variations, 2020 . This paper examines the stochastic maximum principle (SMP) for a forward-backward stochastic control system where the backward state equation is characterized by the backward stochastic differential equation (BSDE) with quadratic growth and the forward
Shaolin Ji, Rundong Xu
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Open Mathematics, 2022 In this paper, our aims are to study the stability with general decay rate of hybrid stochastic fractional differential equations driven by Lévy noise with impulsive effects.
Hou Tingting, Zhang Hui
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Construction of analytical solutions to systems of two stochastic differential equations
Open Mathematics, 2023 A scheme for the stochastization of systems of ordinary differential equations (ODEs) based on Itô calculus is presented in this article. Using the presented techniques, a system of stochastic differential equations (SDEs) can be constructed in such a ...
Navickas Zenonas +4 more
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