A Probabilistic Approach to Large Time Behavior of Mild Solutions of Hamilton-Jacobi-Bellman Equations in Infinite Dimension
Language
en
Article de revue
This item was published in
SIAM Journal on Control and Optimization. 2015, vol. 53, n° 1, p. 378-398
Society for Industrial and Applied Mathematics
English Abstract
We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial ...Read more >
We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial time behaves like a linear term in $T$ shifted with the solution of the associated EBSDE taken at initial time. Moreover we give an explicit speed of convergence, which seems to appear very rarely in literature.Read less <
English Keywords
backward stochastic differential equations
Ornstein-Uhlenbeck operator
HJB equations in infinite dimension
large time behavior
mild solutions
ergodic backward stochastic differential equations
ANR Project
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported