Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

Michael Rockner; Rongchan Zhu; Xiangchan Zhu

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arXiv · 1407.6563

Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions

Michael Rockner·Rongchan Zhu·Xiangchan Zhu

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Abstract

In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g. $d$-dimensional stochastic fractional Navier-Stokes equations with delays, $d$-dimensional stochastic reaction-diffusion equations with delays, $d$-dimensional stochastic porous media equations with delays. Moreover, under local monotonicity conditions for the nonlinear term we obtain the existence and uniqueness of strong solutions to SPDE with delays.

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Michael Rockner, Rongchan Zhu, Xiangchan Zhu. 2014-07-24. Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. https://arxiv.org/abs/1407.6563

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