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

by A. Hudde and M. Hutzenthaler and A. Jentzen and S. Mazzonetto

(Report number 2019-03)

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.

Keywords:

@Techreport{HHJM19_807,
  author = {A. Hudde and M. Hutzenthaler and A. Jentzen and S. Mazzonetto},
  title = {On the Itô-Alekseev-Gr\"obner formula for stochastic differential equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-03.pdf },
  year = {2019}
}

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