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Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces

Marco Fuhrman · Ying Hu · Gianmario Tessitore

67 citations0/0 files storedSIAM Journal on Control and Optimization

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stability and Controllability of Differential Equations

Abstract

In this paper we introduce a new kind of backward stochastic differential equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness, and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the ergodic BSDEs and the associated Hamilton–Jacobi–Bellman equation. Applications are given to the optimal ergodic control of stochastic partial differential equations.

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References

1990Adapted solution of a backward stochastic differential equation 1999Stochastic controls : Hamiltonian systems and HJB equations 1993Backward stochastic differential equations and applications to optimal control 2001Second Order PDE’s in Finite and Infinite Dimension 2002Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control 2013Backward Stochastic Differential Equations 1998On ergodic stochastic control 1998Stability of BSDEs with Random Terminal Time and Homogenization of Semilinear Elliptic PDEs

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2010Ergodic BSDEs under weak dissipative assumptions 2015A Probabilistic Approach to Large Time Behavior of Mild Solutions of HJB Equations in Infinite Dimension 2016Long time asymptotics for fully nonlinear Bellman equations: A backward SDE approach 2017Representation of Homothetic Forward Performance Processes in Stochastic Factor Models via Ergodic and Infinite Horizon BSDE 2009Ergodic BSDEs and related PDEs with Neumann boundary conditions

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