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Reports (Research Report) Year : 2019

Backward Itô-Ventzell and stochastic interpolation formulae


We present a novel backward Itô-Ventzell formula and an extension of the Aleeksev-Gr\"obner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform estimates of the difference between the two stochastic flows when their drift and diffusion functions are not the same, yielding what seems to be the first results of this type for this class of anticipative models. We illustrate the impact of these results in the context of diffusion perturbation theory, interacting diffusions and discrete time approximations
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Dates and versions

hal-02161914 , version 1 (21-06-2019)
hal-02161914 , version 2 (09-07-2019)
hal-02161914 , version 3 (21-10-2019)
hal-02161914 , version 4 (22-06-2020)
hal-02161914 , version 5 (30-04-2021)



Pierre del Moral, Sumeetpal Sidhu Singh. Backward Itô-Ventzell and stochastic interpolation formulae. [Research Report] INRIA. 2019. ⟨hal-02161914v5⟩
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