Stochastic Equations with an Unbounded Operator Coefficient and Multiplicative Noise

Abstract

Under study is a stochastic operator-differential equation with multiplicative noise in the space of Hilbert-valued generalized random variables. Existence and uniqueness of solutions to the Cauchy problem are proved for the case of an unbounded operator coefficient at the white noise. The equation of population dynamics with a stochastically perturbed multiplication operator is presented as an example.