On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows
Probability
2021-11-08 v1
Abstract
In this small note we explicit the relation between Ito and Stratonovich integrals when conditional measure flow components are present in the integrands. The `correction' term involves Lions-type measure derivatives and clarifies which cross-correlations need to be taken into account. We cast the framework in relation to SDEs of mean-field type depending on conditional flows of measure. The result being trivial under full flows of measure.
Keywords
Cite
@article{arxiv.2111.03523,
title = {On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows},
author = {Goncalo dos Reis and Vadim Platonov},
journal= {arXiv preprint arXiv:2111.03523},
year = {2021}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1910.01892