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October 1, 2025Open Access

Stationary distributions of McKean-Vlasov SDEs with jumps: existence, uniqueness, and multiplicity

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Authors

JBJianhai BaoJWJian Wang

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Overview

This paper investigates stationary distributions of McKean-Vlasov SDEs with jumps, revealing existence, uniqueness, and multiplicity.

Key Points

  • Stationary distributions exist under a Lyapunov condition, showcasing the role of Schauder's fixed point theorem.
  • Uniqueness is found consistent with continuous drifts, utilizing weighted total variation and Wasserstein distances.
  • Multiplicity of distributions is demonstrated under locally dissipative conditions, revealing complex behavior in solutions.
  • Examples illustrate scenarios for unique, two, and three stationary distributions in related McKean-Vlasov SDEs.

Cite This Study

Bao et al. (2025) studied this question.

synapsesocial.com/papers/68dd91cbfe798ba2fc4986dfhttps://doi.org/10.48550/arxiv.2504.15898
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