Backward Itô–Ventzell and stochastic interpolation formulae

P. Del Moral and S.S. Singh

Stochastic Processes and their Applications, 2022, vol. 154, issue C, 197-250

Abstract: We present a novel backward Itô–Ventzell formula and an extension of the Alekseev–Gröbner 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, comparisons for solutions of stochastic differential equations, interacting diffusions and discrete time approximations.

Keywords: Stochastic flows; Tangent and Hessian processes; Perturbation semigroups; Skorohod stochastic integral; Malliavin differential; Bismut–Elworthy–Li formulae (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.09.007

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