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Backward Itô–Ventzell and stochastic interpolation formulae

Author

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  • Del Moral, P.
  • Singh, S.S.

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.

Suggested Citation

  • Del Moral, P. & Singh, S.S., 2022. "Backward Itô–Ventzell and stochastic interpolation formulae," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 197-250.
    • Handle: RePEc:eee:spapps:v:154:y:2022:i:c:p:197-250
    DOI: 10.1016/j.spa.2022.09.007
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    References listed on IDEAS

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    1. Bishop, Adrian N. & Del Moral, Pierre & Pathiraja, Sahani D., 2018. "Perturbations and projections of Kalman–Bucy semigroups," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 2857-2904.
    2. James Thompson, 2019. "Derivatives of Feynman–Kac Semigroups," Journal of Theoretical Probability, Springer, vol. 32(2), pages 950-973, June.
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