Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces
Copyright policy )Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces
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 ergodic control of stochastic partial differential equations.
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], hilbert-spaces, stochastic partial differential equations, Probability (math.PR), parabolic equations, Backward Stochastic Differential Equations, Ergodic Control, controlled, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], ergodic control, stochastic optimal control; backward stochastic differential equations; ergodic control; Hamilton-Jacobi-Bellman equation; controlled stochastic partial differential equations, backward stochastic differential equations, FOS: Mathematics, stochastic differential-equations, stochastic optimal control, elliptic pdes, infinite-horizon, Hamilton-Jacobi-Bellman equation, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], hilbert-spaces, stochastic partial differential equations, Probability (math.PR), parabolic equations, Backward Stochastic Differential Equations, Ergodic Control, controlled, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], ergodic control, stochastic optimal control; backward stochastic differential equations; ergodic control; Hamilton-Jacobi-Bellman equation; controlled stochastic partial differential equations, backward stochastic differential equations, FOS: Mathematics, stochastic differential-equations, stochastic optimal control, elliptic pdes, infinite-horizon, Hamilton-Jacobi-Bellman equation, Mathematics - Probability
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