# American Institute of Mathematical Sciences

September  2015, 5(3): 529-555. doi: 10.3934/mcrf.2015.5.529

## Transposition method for backward stochastic evolution equations revisited, and its application

 1 School of Mathematics, Sichuan University, Chengdu 610064, China 2 Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China

Received  May 2014 Revised  April 2015 Published  July 2015

The main purpose of this paper is to improve our transposition method to solve both vector-valued and operator-valued backward stochastic evolution equations with a general filtration. As its application, we obtain a general Pontryagin-type maximum principle for optimal controls of stochastic evolution equations in infinite dimensions. In particular, we drop the technical assumption appeared in [12, Theorem 9.1]. We also establish a Pontryagin-type maximum principle for a stochastic linear quadratic problems.
Citation: Qi Lü, Xu Zhang. Transposition method for backward stochastic evolution equations revisited, and its application. Mathematical Control & Related Fields, 2015, 5 (3) : 529-555. doi: 10.3934/mcrf.2015.5.529
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