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

2014/07/24 by Michael Röckner, Rockner, Michael, Rongchan Zhu +3
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.6563

openalex publication_date 2014/07/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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