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

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  • Bao, Jianhai
  • Wang, Jian

Abstract

In this paper, we are interested in the issues on existence, multiplicity and uniqueness of stationary distributions for McKean-Vlasov SDEs with jumps. In detail, with regarding to McKean-Vlasov SDEs driven by pure jump Lévy processes, we principally (i) explore the existence of stationary distributions via Schauder’s fixed point theorem under an appropriate Lyapunov condition; (ii) demonstrate the multiplicity of stationary distributions under a locally dissipative condition; (iii) tackle the uniqueness of stationary distributions and the convergence to the equilibria as long as the underlying drifts are continuous with respect to the measure variables under the weighted total variation distance and the L1-Wasserstein distance, respectively. In addition, some illustrative examples are provided to show that the associated McKean-Vlasov SDEs possess a unique, two and three stationary distributions, respectively.

Suggested Citation

  • Bao, Jianhai & Wang, Jian, 2026. "Stationary distributions of McKean-Vlasov SDEs with jumps: Existence, multiplicity and uniqueness," Stochastic Processes and their Applications, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:spapps:v:198:y:2026:i:c:s0304414926000992
    DOI: 10.1016/j.spa.2026.104967
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