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Mathematics > Probability
Title: Itō and Itō-Wentzell chain rule for flows of conditional laws of continuous semimartingales: an easy approach
(Submitted on 17 Apr 2024 (v1), last revised 18 Apr 2024 (this version, v2))
Abstract: We provide a general It\=o\,-Wentzell formula for a random field of maps on the Wasserstein space of probability measures, defined by continuous semimartingales, and evaluated along the flow of conditional distributions of another continuous semimartingale. Our method follows standard arguments of It\=o calculus, and thus bypasses the approximation by empirical measures commonly used in the existing literature. As an application, we derive the dynamic programming equation for a mean field stochastic control problem with common noise.
Submission history
From: Nizar Touzi Pr [view email][v1] Wed, 17 Apr 2024 02:37:21 GMT (22kb)
[v2] Thu, 18 Apr 2024 04:01:31 GMT (22kb)
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