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Harnack Inequalities for Mean-Field G-Stochastic Differential Equations with Multiplicative Noise

Author

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  • Xiyuan Su

    (Shanghai University
    Shanghai University)

  • Menglin Xu

    (Shanghai University
    Shanghai University)

  • Fen-Fen Yang

    (Shanghai University
    Shanghai University)

Abstract

In this paper, we investigate the existence and uniqueness of the solution for mean-field stochastic differential equations (SDEs) with multiplicative noise starting from a random variable under the G-framework by using Banach’s fixed-point theorem. Moreover, Harnack and log-Harnack inequalities are established by means of coupling by change of measures.

Suggested Citation

  • Xiyuan Su & Menglin Xu & Fen-Fen Yang, 2025. "Harnack Inequalities for Mean-Field G-Stochastic Differential Equations with Multiplicative Noise," Journal of Theoretical Probability, Springer, vol. 38(2), pages 1-29, June.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:2:d:10.1007_s10959-025-01409-w
    DOI: 10.1007/s10959-025-01409-w
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    References listed on IDEAS

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    5. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
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