Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions
Probability
2014-07-25 v1 Analysis of PDEs
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. -dimensional stochastic fractional Navier-Stokes equations with delays, -dimensional stochastic reaction-diffusion equations with delays, -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.
Keywords
Cite
@article{arxiv.1407.6563,
title = {Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions},
author = {Michael Rockner and Rongchan Zhu and Xiangchan Zhu},
journal= {arXiv preprint arXiv:1407.6563},
year = {2014}
}