General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

Details General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

2012-04-15

arxiv.org/abs/1204.3275v1

Mathematics

Optimization and Control

56 pages

Scientific paper

The main purpose of this paper is to give a solution to a long-standing unsolved problem in stochastic control theory, i.e., to establish the Pontryagin-type maximum principle for optimal controls of infinite dimensional stochastic evolution equations with the control variable appeared in both the drift and the diffusion terms and with possibly nonconvex control domains. The key to do this is a correct formulation of operator-valued backward stochastic evolution equations (BSEEs for short), and how to define their solutions. General vector-valued BSEEs are studied as well. The solutions to both vector-valued and operator-valued BSEEs are defined in the sense of transposition, and the corresponding well-posedness results are presented.

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