On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows

Goncalo dos Reis; Vadim Platonov

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arXiv · 2111.03523

On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows

Goncalo dos Reis·Vadim Platonov

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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.

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Goncalo dos Reis, Vadim Platonov. 2021-11-05. On the relation between Stratonovich and Ito integrals with functional integrands of conditional measure flows. https://arxiv.org/abs/2111.03523

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