TY - JOUR
T1 - Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions
AU - Röckner, Michael
AU - Zhu, Rongchan
AU - Zhu, Xiangchan
N1 - Publisher Copyright:
© 2015 Elsevier Ltd. All rights reserved.
PY - 2015/6/18
Y1 - 2015/6/18
N2 - 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.
AB - 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.
KW - Local monotonicity
KW - Martingale problem
KW - Stochastic functional equation
KW - Stochastic partial differential
KW - equations with delay
UR - http://www.scopus.com/inward/record.url?scp=84935926088&partnerID=8YFLogxK
U2 - 10.1016/j.na.2015.05.019
DO - 10.1016/j.na.2015.05.019
M3 - Article
AN - SCOPUS:84935926088
SN - 0362-546X
VL - 125
SP - 358
EP - 397
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -