Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

Ton Viet Ta; Yoshitaka Yamamoto; Atsushi Yagi

paper

Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

arXiv:1508.07431

Abstract

We study a stochastic linear evolution equation $d X + A (t) X d t = F (t) d t + G (t) d w_{t}$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The abstract results are applied to stochastic diffusion equations.

27 pages, to appear in Funkcialaj Ekvacioj