Singular Degenerate SDEs: Well-Posedness and Exponential Ergodicity

Published 28 Apr 2023 in math.PR | (2305.00129v1)

Abstract: The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform exponential ergodicity are derived for a class of singular degenerated McKean-Vlasov SDEs.

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