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

Röckner M, Zhu R, Zhu X. Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. Nonlinear Analysis Theory Methods & Applications. 2015;125:358-397.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. (C) 2015 Elsevier Ltd. All rights reserved