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arXiv:2010.05288 [math.PR]AbstractReferencesReviewsResources

Itô's formula for flow of measures on semimartingales

Xin Guo, Huyên Pham, Xiaoli Wei

Published 2020-10-11Version 1

We state It\^o's formula along a flow of probability measures associated with general semimartingales. This extends recent existing results for flow of measures on It\^o processes. Our approach is to first prove It\^o's formula for cylindrical polynomials and then use function approximation for the general case. Some applications to McKean- Vlasov controls of jump-diffusion processes and McKean-Vlasov singular controls are developed.

Categories: math.PR, math.OC
Subjects: 60H30, 60K35, 93E20
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