On Stochastic Evolution Equations with non-Lipschitz Coefficients

Xicheng Zhang

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On Stochastic Evolution Equations with non-Lipschitz Coefficients

Xicheng Zhang

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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.

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Xicheng Zhang. 2008-01-10. On Stochastic Evolution Equations with non-Lipschitz Coefficients. https://arxiv.org/abs/math/0703260

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