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Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by L\'evy noise

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arxiv 2010.08585 v1 pith:TQ7IEPOZ submitted 2020-10-16 math.PR cs.NAmath.NA

Neelima , Sani Biswas , Chaman Kumar , Gonçalo dos Reis , Christoph Reisinger This is my paper · ORCID
classification math.PRcs.NAmath.NA
keywords drivenequationseulermckean-vlasovnoisetamedwell-posednessdifferential
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abstract

We prove the well-posedness of solutions to McKean-Vlasov stochastic differential equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy measure is not required to be finite. The drift, diffusion and jump coefficients are allowed to be random, can grow super-linearly in the state variable, and all may depend on the marginal law of the solution process. We provide a propagation of chaos result under more relaxed conditions than those existing in the literature, and consistent with our well-posedness result. We propose a tamed Euler scheme for the associated interacting particle system and prove that the rate of its strong convergence is arbitrarily close to $1/2$. As a by-product, we also obtain the corresponding results on well-posedness, propagation of chaos and strong convergence of the tamed Euler scheme for McKean-Vlasov stochastic delay differential equations (SDDE) and McKean-Vlasov stochastic differential equations with Markovian switching (SDEwMS), both driven by L\'evy noise. Furthermore, our results on tamed Euler schemes are new even for ordinary SDEs driven by L\'evy noise and with super-linearly growing coefficients.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Euler-type methods for Levy-driven McKean-Vlasov SDEs with super-linear coefficients: mean-square error analysis

    math.NA 2025-09 conditional novelty 6.0 of 10

    A unified family of Euler-type schemes for Lévy-driven McKean-Vlasov SDEs is shown to converge in mean square with L2 order arbitrarily close to 1/2 under super-linear coefficients.

  2. Ergodicity of conditional McKean-Vlasov jump diffusions

    math.PR 2025-09 conditional novelty 6.0 of 10

    Conditional McKean-Vlasov jump diffusions are exponentially contractive in law, and the contraction rate improves as jump noise intensity grows.

  3. The adaptive EM schemes for McKean-Vlasov SDEs with common noise in finite and infinite horizons

    math.NA 2025-08 conditional novelty 6.0 of 10

    An adaptive Euler-Maruyama scheme for McKean-Vlasov SDEs with common noise is proved to converge strongly at rate δ^(1/2) in finite and infinite horizons.

  4. Convergence and stability of truncated Euler-Maruyama algorithm for stochastic proportional delay Mckean-Vlasov models with jump process

    math.NA 2026-07 conditional novelty 5.0 of 10

    The authors prove convergence-rate and almost-sure-exponential-stability bounds for a truncated Euler scheme applied to superlinear McKean-Vlasov proportional-delay SDEs with Lévy jumps.

  5. On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients

    math.NA 2025-02 conditional novelty 5.0 of 10

    A general class of modified Euler methods, including tanh and sin Euler schemes, is shown to converge with strong order 1/2 for McKean-Vlasov SDEs with super-linear coefficients.

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