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

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• 作者：Andrea Cosso^a ; ^{cosso@math.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author} ; Marco Fuhrman^b ; ^{marco.fuhrman@polimi.it" class="auth_mail" title="E-mail the corresponding author} ; Huyê ; n Pham^a ; ^c ; ^{pham@math.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60H30 ; 60J60 ; 49J20
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：126
• 期：7
• 页码：1932-1973
• 全文大小：427 K

文摘

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.