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arXiv · 2505.13155

It\^o-Wentzell-Lions formulae for flows of full and conditional measures on semimartingales

Liu Jisheng·Zhang Jing
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Abstract

In this paper, we establish the It\^o-Wentzell-Lions formulae for flows of both full and conditional measures on general semimartingales. This generalizes the existing works on flows of measures on It\^o processes. The key technical components involve an appropriate approximation of random fields by cylindrical functions and localization techniques. Moreover, we present the specific formulae in two special cases, including It\^o-Wentzell-Lions formulae for time-space-measure-dependent functions and for functions driven by Poisson random measures.

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Liu Jisheng, Zhang Jing. 2025-05-19. It\^o-Wentzell-Lions formulae for flows of full and conditional measures on semimartingales. https://arxiv.org/abs/2505.13155

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