This study reveals a log-Harnack inequality in stochastic differential equations with infinite memory, indicating new results even without distribution dependence.
We establish an asymptotic log-Harnack inequality for stochastic differential equations on ᵈ whose coefficients depend on the path and distribution for the whole history, allowing the drift to contain a Dini continuous term. The result is new even in the distribution-independent case.
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Xiaoyu Zhao (2025) studied this question.
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