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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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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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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.
Hun O, Mun-chol Kim, Chol-Gyu Pak
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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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The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation [PDF]
Indiana University Mathematics Journal, 2019 One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+\mathrm{ div}(D(x)b(u)u)=0, \ t\ge0, \ x\in\mathbb{R}^d,\hspace{1cm} (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and $b ...
V. Barbu, M. Rockner
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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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The influence of the noise on the exact solutions of a Kuramoto-Sivashinsky equation
Open Mathematics, 2022 In this article, we take into account the stochastic Kuramoto-Sivashinsky equation forced by multiplicative noise in the Itô sense. To obtain the exact stochastic solutions of the stochastic Kuramoto-Sivashinsky equation, we apply the G′G\frac{{G ...
Albosaily Sahar +4 more
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Open Mathematics, 2022 The Picard iteration method is used to study the existence and uniqueness of solutions for the stochastic Volterra-Levin equation with variable delays. Several sufficient conditions are specified to ensure that the equation has a unique solution.
Jin Shoubo
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Demonstratio Mathematica, 2023 In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed.
Mohammed Wael W. +2 more
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Averaging principle for two-time-scale stochastic differential equations with correlated noise
Open Mathematics, 2022 This article is devoted to studying the averaging principle for two-time-scale stochastic differential equations with correlated noise. By the technique of multiscale expansion of the solution to the backward Kolmogorov equation and consequent ...
Jiang Tao, Liu Yancai
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