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arXiv · 2608.00370

Continuity of measure-theoretic entropy for stochastic differential equations

Zhenxin Liu·Lixin Zhang
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Abstract

For stochastic differential equations, we establish a relationship between the measure-theoretic entropy of the stochastic flow and the rate of volume growth of stable submanifolds under iteration. By combining the result of Kifer and Yomdin (1988), we show that under a suitable integrability condition, for systems with $C^{\infty}$ coefficients, the measure-theoretic entropy is upper semicontinuous with respect to the coefficients of SDEs.

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Zhenxin Liu, Lixin Zhang. 2026-08-01. Continuity of measure-theoretic entropy for stochastic differential equations. https://arxiv.org/abs/2608.00370

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