Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. (September 2015) - Röckner, Michael; Zhu, Rongchan; Zhu, Xiangchan
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 terms we obtain the existence and uniqueness of strong solutions to SPDE with delays.