We establish existence and uniqueness of an optimal control for a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control and quadratic dependence on control of the cost function. We propose an N-particle Markovian optimal control problem approximating the McKean-Vlasov one and prove the convergence in relative entropy and total variation of the law of the former to the law of the latter when N goes to infinity.
Mean-Field Limit For A Class Of Stochastic Ergodic Control Problems
De Vecchi F. C.
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2022-01-01
Abstract
We establish existence and uniqueness of an optimal control for a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control and quadratic dependence on control of the cost function. We propose an N-particle Markovian optimal control problem approximating the McKean-Vlasov one and prove the convergence in relative entropy and total variation of the law of the former to the law of the latter when N goes to infinity.File in questo prodotto:
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