Computing the invariant distribution of McKean-Vlasov SDEs by ergodic
 simulation

Jean-François Chassagneux; Gilles Pagès

doi:10.48550/arxiv.2406.13370

June 19, 2024Open Access

Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation

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Key Points

Invariance is achieved through a new scheme that computes the invariant distribution effectively, enhancing existing methods.
Key convergence results show rates for the Wasserstein distance in quadratic mean, ensuring reliability and precision.
The approach utilizes ergodic simulation to handle McKean-Vlasov SDEs, focusing on those with a uniform confluence property for accuracy of outcomes and computations. If adopted broadly, these methods can greatly influence how stochastic differential equations are approached in various fields.

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Implication

Ergodic simulation computes the invariant distribution of McKean-Vlasov SDEs, suggesting effective convergence methods.

Abstract

We design a fully implementable scheme to compute the invariant distribution of ergodic McKean-Vlasov SDE satisfying a uniform confluence property. Under natural conditions, we prove various convergence results notably we obtain rates for the Wasserstein distance in quadratic mean and almost sure sense.

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Chassagneux et al. (2024) studied this question.

synapsesocial.com/papers/68e642a2b6db6435875d45b6 https://doi.org/10.48550/arxiv.2406.13370

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Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation

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Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation

Key Points

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Implication

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