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Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations

Author

Listed:
  • Xing Huang

    (Tianjin University)

  • Xiaochen Ma

    (Tianjin University)

Abstract

By investigating the regularity of the nonlinear semigroup $$P_t^*$$ P t ∗ associated with the distribution dependent second-order stochastic differential equations, the Harnack inequality is derived when the drift is Lipschitz continuous in the measure variable under the distance induced by the functions being $$\beta $$ β -Hölder continuous (with $$\beta > \frac{2}{3}$$ β > 2 3 ) on the degenerate component and square root of Dini continuous on the non-degenerate one. The results extend the existing ones in which the drift is Lipschitz continuous in $$L^2$$ L 2 -Wasserstein distance.

Suggested Citation

  • Xing Huang & Xiaochen Ma, 2024. "Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3152-3176, November.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01346-0
    DOI: 10.1007/s10959-024-01346-0
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    References listed on IDEAS

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    1. Wang, Feng-Yu, 2018. "Distribution dependent SDEs for Landau type equations," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 595-621.
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