English

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