A PROBABILISTIC APPROACH TO LARGE TIME BEHAVIOR OF MILD SOLUTIONS OF HJB EQUATIONS IN INFINITE DIMENSION

作者：Hu Ying^*; Madec Pierre Yves; Richou Adrien

来源：SIAM Journal on Control and Optimization, 2015, 53(1): 378-398.

DOI：10.1137/140976091

• backward stochastic differential equations
• ergodic backward stochastic differential equations
• HJB equations in infinite dimension
• large time behavior
• mild solutions
• Ornstein-Uhlenbeck operator

We study the large time behavior of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a backward SDE in finite horizon T taken at initial time behaves like a linear term in T shifted with the solution of the associated ergodic backward SDE taken at initial time. Moreover we give an explicit rate of convergence, which seems to be new to our best knowledge.

• 出版日期2015