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

Andrea Cosso, Marco Fuhrman and Huyên Pham

Stochastic Processes and their Applications, 2016, vol. 126, issue 7, 1932-1973

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.

Keywords: Hamilton–Jacobi–Bellman type equation; Stochastic control; Large time behavior; Backward SDE; Ergodic type Bellman equation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spa.2015.12.009

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