Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 527, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127404
Keywords
McKean-Vlasov equations; Hamilton-Jacobi-Bellman equations; Viscosity solutions; Ergodic control
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We study the ergodic control problem for McKean-Vlasov stochastic differential equations and establish the existence and uniqueness of the viscosity solution to the associated fully nonlinear HJB equation in a lifted sense. Moreover, we demonstrate the convergence of the solutions of finite-horizon time-averaging optimal control problems to that of the ergodic control problem as the time horizon tends to infinity. Our results rely on dissipativity conditions and dissipativity-like conditions on the distribution variables of both drift and diffusion coefficients. (c) 2023 Elsevier Inc. All rights reserved.
We consider the ergodic control problem for McKean-Vlasov stochastic differential equations and prove the existence and uniqueness of the viscosity solution to the associated fully nonlinear HJB equation in a lifted sense. Furthermore, as the time horizon goes to infinity, we show that the solutions of finite-horizon time-averaging optimal control problems converge to that of the ergodic control problem. Our results require dissipativity conditions and dissipativity-like conditions on distribution variables of both drift and diffusion coefficients.(c) 2023 Elsevier Inc. All rights reserved.
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