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

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.

19 pages

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Cited by in corpus (3)

• On the Itô-Alekseev-Gröbner formula for stochastic differential equations
• Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives
• A second order analysis of McKean-Vlasov semigroups