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Mathematics > Probability

arXiv:1812.09857 (math)
[Submitted on 24 Dec 2018 (v1), last revised 27 May 2024 (this version, v2)]

Title:On the Itô-Alekseev-Gröbner formula for stochastic differential equations

Authors: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 Itô process. The introduced formula essentially generalizes both the classical Alekseev-Gröbner formula from the literature on deterministic differential equations as well as the classical Itô formula from stochastic analysis. The proposed Itô-Alekseev-Gröbner formula is a powerful tool for deriving strong approximation rates for perturbations and approximations of stochastic ordinary and partial differential equations.
Comments: 19 pages
Subjects: Probability (math.PR)
MSC classes: 60H10
Cite as: arXiv:1812.09857 [math.PR]
  (or arXiv:1812.09857v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.09857
Journal reference: Ann. Inst. H. Poincaré Probab. Statist. 60 (2), 904-922, (2024)
Related DOI: https://doi.org/10.1214/21-AIHP1199

Submission history

From: Martin Hutzenthaler [view email]
[v1] Mon, 24 Dec 2018 07:53:06 UTC (32 KB)
[v2] Mon, 27 May 2024 13:53:01 UTC (69 KB)
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