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arXiv · 1812.09857

On the It\^o-Alekseev-Gr\"obner formula for stochastic differential equations

Anselm Hudde·Martin Hutzenthaler·Arnulf Jentzen·Sara Mazzonetto
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Abstract

In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an It\^o process. The introduced formula essentially generalizes both the classical Alekseev-Gr\"obner formula from the literature on deterministic differential equations as well as the classical It\^o formula from stochastic analysis. The proposed It\^o-Alekseev-Gr\"obner formula is a powerful tool for deriving strong approximation rates for perturbations and approximations of stochastic ordinary and partial differential equations.

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Anselm Hudde, Martin Hutzenthaler, Arnulf Jentzen, Sara Mazzonetto. 2018-12-24. On the It\^o-Alekseev-Gr\"obner formula for stochastic differential equations. https://doi.org/10.1214/21-aihp1199

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