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arXiv · 2301.08029

Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: wellposedness, propagation of chaos, averaging principle

Jinghai Shao·Taoran Tian·Shen Wang
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Abstract

We investigate the conditional McKean-Vlasov stochastic differential equations with jumps and Markovian regime-switching. We establish the strong wellposedness using L2-Wasser-stein distance on the Wasserstein space. Also, we establish the propagation of chaos for the associated mean-field interaction particle system with common noise and provide an explicit bound on the convergence rate. Furthermore, an averaging principle is established for two time-scale conditional McKean-Vlasov equations, where much attention is paid to the convergence of the conditional distribution term.

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Jinghai Shao, Taoran Tian, Shen Wang. 2023-01-19. Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: wellposedness, propagation of chaos, averaging principle. https://arxiv.org/abs/2301.08029

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