On Stochastic Evolution Equations with non-Lipschitz Coefficients

2007/03/09 by Xicheng Zhang, Zhang, Xicheng · 2 citations
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #60H15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #math.PR #msc:60H15

paper · pdf · doi:10.48550/arxiv.math/0703260

Add two applications and correct some errors

openalex publication_date 2007/03/09 · arxiv created 2008/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that is, backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations. In particular, the results can be used to treat a large class of quasi-linear stochastic equations, which includes the reaction diffusion and porous medium equations.

Cited by

• Well-posedness of Fractional Stochastic p-Laplace Equations Driven by Superlinear Transport Noise
• Martingale Solutions of Fractional Stochastic Reaction-Diffusion Equations Driven by Superlinear Noise

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