On the infinite time horizon approximation for L\'evy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

Ngoc Khue Tran; Trung-Thuy Kieu; Duc-Trong Luong; Hoang-Long Ngo

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arXiv · 2401.03977

On the infinite time horizon approximation for L\'evy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

Ngoc Khue Tran·Trung-Thuy Kieu·Duc-Trong Luong·Hoang-Long Ngo

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Abstract

This paper studies the numerical approximation for McKean-Vlasov stochastic differential equations driven by L\'evy processes. We propose a tamed-adaptive Euler-Maruyama scheme and consider its strong convergence in both finite and infinite time horizons when applying for some classes of L\'evy-driven McKean-Vlasov stochastic differential equations with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients.

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Ngoc Khue Tran, Trung-Thuy Kieu, Duc-Trong Luong, Hoang-Long Ngo. 2024-01-08. On the infinite time horizon approximation for L\'evy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients. https://arxiv.org/abs/2401.03977

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