Infinite Horizon Optimal Control Problem for Stochastic Evolution Equations in Hilbert Spaces

• DOI: 10.1007/s10883-015-9307-2
• Publication Date: 2015-11-09T01:10:50Z
• Authors: Jianjun Zhou
• Keywords: Stochastic control; Heat equation

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated infinite horizon backward stochastic differential equations with quadratic growth. As an application, an optimal control of stochastic heat equation is also given.