Large Deviations and Exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts

Daniel Adams, Gonçalo dos Reis, Romain Ravaille, William Salkeld and Julian Tugaut

Stochastic Processes and their Applications, 2022, vol. 146, issue C, 264-310

Abstract: We study reflected McKean–Vlasov diffusions over a convex, non-bounded domain with self-stabilising coefficients that do not satisfy the classical Wasserstein Lipschitz condition. We establish existence and uniqueness results for this class and address the propagation of chaos. Our results are of wider interest: without the McKean–Vlasov component they extend reflected SDE theory, and without the reflective term they extend the McKean–Vlasov theory.

Keywords: Reflected McKean–Vlasov equations; Self-stabilising diffusions; Super-linear growth; Freidlin–Wentzell Large Deviations Principle; Eyring–Kramer law (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2021.12.017

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