Stochastic evolution equations with multiplicative noise

Tijana Levajkovic, Stevan Pilipovic, Dora Selesi, Milica Zigic

Published 2023-03-10Version 1

We study parabolic stochastic partial differential equations (SPDEs), driven by two types of operators: one linear closed operator generating a $C_0-$semigroup and one linear bounded operator with Wick-type multiplication, all of them set in the infinite dimensional space framework of white noise analysis. We prove existence and uniqueness of solutions for this class of SPDEs. In particular, we also treat the stationary case when the time-derivative is equal to zero.