no. 7
Probabilités
A backward Itô–Ventzell formula with an application to stochastic interpolation
Del Moral, Pierre1  ; Singh, Sumeetpal S.2
1 INRIA Bordeaux Research Center, University of Bordeaux, Talance, France
2 Department of Engineering, University of Cambridge, United Kingdom
Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 881-886.

This Note and its extended version [7] present a novel backward Itô–Ventzell formula and an extension of the Aleeksev–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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.110
Classification : 47D07, 93E15, 60H07
Del Moral, Pierre 1 ; Singh, Sumeetpal S. 2

1 INRIA Bordeaux Research Center, University of Bordeaux, Talance, France
2 Department of Engineering, University of Cambridge, United Kingdom 
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Del Moral, Pierre; Singh, Sumeetpal S. A backward Itô–Ventzell formula with an application to stochastic interpolation. Comptes Rendus. Mathématique, Tome 358 (2020) no. 7, pp. 881-886. doi : 10.5802/crmath.110. http://www.numdam.org/articles/10.5802/crmath.110/

[1] Alekseev, Vladimir An estimate for the perturbations of the solution of ordinary differential equations, Vestn. Mosk. Univ. (1961) no. 2, pp. 28-36 | MR

[2] Arnaudon, Marc; Del Moral, Pierre A duality formula and a particle Gibbs sampler for continuous time Feynman–Kac measures on path spaces (2018) (https://arxiv.org/abs/1805.05044)

[3] Arnaudon, Marc; Del Moral, Pierre A variational approach to nonlinear and interacting diffusions, Stochastic Anal. Appl., Volume 37 (2019) no. 5, pp. 717-748 | DOI | MR | Zbl

[4] Arnaudon, Marc; Del Moral, Pierre A second order analysis of McKean–Vlasov semigroups, 2020 (To appear in The Annals of Applied Probability)

[5] Bishop, Adrian N.; Del Moral, Pierre; Niclas, Angèle A perturbation analysis of stochastic matrix Riccati diffusions, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 56 (2020) no. 2, pp. 884-916 | DOI | MR | Zbl

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[7] Del Moral, Pierre; Sidhu Singh, Sumeetpal Backward Itô–Ventzell and stochastic interpolation formulae (2019) (https://hal.archives-ouvertes.fr/hal-02161914v4)

[8] Nualart, David The Malliavin calculus and related topics, Probability and Its Applications, 1995, Springer, 2006 | Zbl

[9] Ocone, Daniel; Pardoux, Etienne A generalized Itô–Ventzell formula. Application to a class of anticipating stochastic differential equations, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 25 (1989) no. 1, pp. 39-71 | Numdam | Zbl

[10] Pardoux, Etienne; Protter, Philip E. A two-sided stochastic integral and its calculus, Probab. Theory Relat. Fields, Volume 76 (1987) no. 1, pp. 15-49 | DOI | MR | Zbl

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