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Backward Itô-Ventzell and stochastic interpolation formulae

Pierre del Moral 1 Sumeetpal Sidhu Singh 2
1 ASTRAL - Méthodes avancées d’apprentissage statistique et de contrôle
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, Bordeaux INP - Institut Polytechnique de Bordeaux, Naval Group
Abstract : 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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Submitted on : Friday, April 30, 2021 - 10:58:44 AM
Last modification on : Friday, February 4, 2022 - 3:23:37 AM


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  • HAL Id : hal-02161914, version 5
  • ARXIV : 1906.09145



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



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