Stochastic Bernoulli equation on the algebra of generalized functions

Abstract

UDC 519.21 Based on the topological dual space ℱ θ * ( S ' ℂ ) of the space of entire functions with θ -exponential growth of finite type, we introduce the generalized stochastic Bernoulli–Wick differential equation (or the stochastic Bernoulli equation on the algebra of generalized functions) by using the Wick product of elements in ℱ θ * ( S ' ℂ ) . This equation is an infinite-dimensional stochastic distributions analog of the classical Bernoulli differential equation. This stochastic differential equation is solved and exemplified by several examples.