We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control affecting both drift and diffusion coefficients. We prove that, as time horizon goes to infinity, the long run average solution is characterized by a nonlinear ergodic equation. Our results hold under dissipativity conditions, and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments relying on new backward SDE representation for nonlinear parabolic, elliptic and ergodic equations.

Long time asymptotics for fully nonlinear Bellman equations: A backward SDE approach / A. Cosso, M. Fuhrman, H. Pham. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 126:7(2016), pp. 1932-1973. [10.1016/j.spa.2015.12.009]

Long time asymptotics for fully nonlinear Bellman equations: A backward SDE approach

A. Cosso;M. Fuhrman
Secondo
;
2016

Abstract

We study the large time behavior of solutions to fully nonlinear parabolic equations of Hamilton-Jacobi-Bellman type arising typically in stochastic control theory with control affecting both drift and diffusion coefficients. We prove that, as time horizon goes to infinity, the long run average solution is characterized by a nonlinear ergodic equation. Our results hold under dissipativity conditions, and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments relying on new backward SDE representation for nonlinear parabolic, elliptic and ergodic equations.
Backward SDE; Ergodic type Bellman equation; Hamilton-Jacobi-Bellman type equation; Large time behavior; Stochastic control; Statistics and Probability;
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/472451
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