Pontryagin-type stochastic maximum principle of stochastic evolution equations with a random generator

Abstract:

In this paper,we establish a Pontryagin-type maximum principle for a control stochastic evolution equation with a random generator and a convex control domain. Given p>=2, the existence and uniqueness of mild solutions to the control system are obtained by using the Malliavin calculus. To study the well-posedness of the adjoint systems when 1