Về một điều kiện thác triển liên tục nghiệm phương trình vi phân ngẫu nhiên trong không gian Hilbert

Abstract

We study about mild solutions and weak solutions of non-linear stochastic differential equations (SDEs) in Hilbert spaces for the case of family of time-dependent and unbounded operators and get some conditions that weak solutions to become mild solutions and vice versa. We also study continuously extension of mild solutions on Hilbert spaces. Our equation and concept of solutions are arisen as a stochastic partial differential equation (SPDE) in industrial mathematics.