Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations [PDF]
, 2007 Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability.
Yuan, C. +4 more
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Stochastic flows for SDEs with non-Lipschitz coefficients
Bulletin des Sciences Mathématiques, 2003 A stochastic differential equation \[ dX_t=\sum_{n=1}^\infty\sigma_n(X_t)dW_t^n+b(X_t)dt,\quad X_0=x\in{\mathbb R}, \] is considered, where \(W^n\) are Brownian motions, \(n=1,2,\dots\), and none of the \(\sigma_n\)'s or \(b\) are Lipschitz. Conditions on coefficients are given which imply that the solution is a.s.\ continuous in \(x\) and \(t\) for ...
Ren, Jiagang, Zhang, Xicheng
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Stochastic invariance for hybrid stochastic differential equation with non-Lipschitz coefficients
AIMS Mathematics, 2020 In the paper, the following stochastic differential equation \[ d X(t) = f(X(t),i)dt+g(X(t),i)dw(t), \quad 1\leq i\leq N, \tag{1} \] with the initial condition \[ \qquad X(0)= x\in \mathbb{R}^{d} \tag{2} \] is considered. In (1)-(2), \(\mathcal{M}=\left\{ 1,2,3,\ldots,N \right\}\), \(f:\mathbb{R}^{d}\times\mathcal{M}\to \mathbb{R}^{d}\) and \(g:\mathbb{
Chunhong Li, Sanxing Liu
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A Zvonkin's transformation for stochastic differential equations with singular drift and applications [PDF]
, 2021 In this paper, a new Zvonkin-type transformation is given for stochastic differential equations with singular and Lipschitz drifts by establishing the localized $L^p$-$L^q$ estimate and Sobolev estimates for parabolic partial differential equations ...
Chenggui Yuan
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An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients [PDF]
, 2015 In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading
Menoukeu Pamen, Olivier +1 more
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Generalized Stochastic Burgers' Equation with Non-Lipschitz Diffusion Coefficient
Communications on Stochastic Analysis, 2019 Summary: We study the existence of weak solutions to the one-dimensional generalized stochastic Burgers' equation with polynomial nonlinearity perturbed by space-time white noise with Dirichlet boundary conditions and \(\alpha\)-Hölder continuous coefficient in noise term, where \(\alpha\in[1/2,1)\).
Kumar, Vivek, Giri, Ankik Kumar
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STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND NON-LIPSCHITZ COEFFICIENTS
, 2020 Stochastic Volterra integral equations with jumps (SVIEs) have become very common and widely used in numerous branches of science, due to their connections with mathematical finance, biology, engineering and so on. In this paper, we apply the successive approximation method to investigate the existence and uniqueness of solutions to the SVIEs driven by
Khalaf, Anas Dheyab, Wang, Xiangjun
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Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients [PDF]
Statistics & Probability Letters, 2022 23 ...
Ruifang Wang, Yong Xu, Hongge Yue
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A class of degenerate stochastic differential equations with non-Lipschitz coefficients [PDF]
Proceedings - Mathematical Sciences, 2013 13 ...
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Reflected BSDEs with default time and irregular obstacles
Comptes Rendus. MathématiqueIn this note, we study reflected backward stochastic differential equations with a default time, where the reflecting obstacle is not necessarily right-continuous.
Elmansouri, Badr
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