A note on continuously extended solutions of stochastic differential equations on Hilbert spaces
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.