Existence of β-martingale solutions of stochastic evolution functional equations of parabolic type with measurable locally bounded coefficients

摘要

We prove a theorem on the existence of β-martingale solutions of stochastic evolution functional equations of parabolic type with Borel measurable locally bounded coefficients. A β-martingale solution of a stochastic evolution functional equation is understood as a martingale solution of a stochastic evolution functional inclusion constructed on the basis of the equation. We find sufficient conditions for the existence of β-martingale solutions that do not blow up in finite time.