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arXiv · 2502.13353

Path-Distribution Dependent SDEs: Well-Posedness and Asymptotic Log-Harnack Inequality

Feng-Yu Wang·Chenggui Yuan·Xiao-Yu Zhao
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Abstract

We consider stochastic differential equations on $\mathbb R^d$ with coefficients depending on the path and distribution for the whole history. Under a local integrability condition on the time-spatial singular drift, the well-posedness and Lipschitz continuity in initial values are proved, which is new even in the distribution independent case. Moreover, under a monotone condition, the asymptotic log-Harnack inequality is established, which extends the corresponding result of [5] derived in the distribution independent case.

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Feng-Yu Wang, Chenggui Yuan, Xiao-Yu Zhao. 2025-02-19. Path-Distribution Dependent SDEs: Well-Posedness and Asymptotic Log-Harnack Inequality. https://arxiv.org/abs/2502.13353

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