Harnack Inequality for Distribution Dependent Second-Order Stochastic Differential Equations

Xing Huang () and Xiaochen Ma ()
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Xing Huang: Tianjin University
Xiaochen Ma: Tianjin University

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3152-3176

Abstract: 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.

Keywords: Second-order SDEs; Distribution dependent SDEs; Harnack inequality; Hölder continuity; Square root of Dini continuity; 60H10; 60H15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01346-0

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