AIP Advances, 2023 Stochastic methods significantly solve stochastic differential equations such as stochastic equations with a delay, stochastic fractional and fractal equations, stochastic partial differential equations, and many more.
Wafa F. Alfwzan +5 more
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Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations [PDF]
, 2004 We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism ...
Kolokoltsov, V. N. (Vasiliĭ Nikitich) +10 more
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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform
Современная математика: Фундаментальные направления, 2021 The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations - stochastic differential equations (SDEs) - and deterministic equations for the ...
I. V. Melnikova +2 more
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On stochastic differential equations and a generalised Burgers equation [PDF]
, 2012 In this paper, we discuss a link of Itˆo’s stochastic differential equa- tions to nonlinear partial differential equations of Burgers type. Un- der certain conditions, we derive a generalised Burgers equation from a stochastic differential equation.
Wu, JiangLun, Yang, Wei
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Approximate solutions of hybrid stochastic pantograph equations with Levy jumps [PDF]
, 2013 We investigate a class of stochastic pantograph differential equations with Markovian switching and Levy jumps. We prove that the approximate solutions converge to the true solutions in 퐿 2 sense as well as in probability under local Lipschitz condition ...
Mao, Wei, Mao, Xuerong
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Fractional SDEs with stochastic forcing: Existence, uniqueness, and approximation
Nonlinear Analysis, 2023 In this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term.
Kęstutis Kubilius
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Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching [PDF]
, 2008 The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching.
Yuan, Chenggui +7 more
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Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
Journal of Applied Mathematics, 2012 We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s ...
Li Chen, Zhen Wu, Zhiyong Yu
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Models of stochastic dynamics of development of industrial enterprises with lagging internal and external investments [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 The article proposes new stochastic models of the dynamic development of enterprises that restore their production at the expense of internal and external lagging investments.
Alexander L. Saraev, Leonid A. Saraev
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Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations [PDF]
, 2013 A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs).
Wu, Fuke +2 more
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