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- W2992667609 abstract "In this thesis we establish the Ito-Alekseev-Grobner formula which can be regarded as a generalization of the Alekseev-Grobner lemma and Ito's lemma.Analogous to the well-known deterministic case of the Alekseev-Grobner lemma, this formula allows us to estimate the global error between the exact solution of a stochastic differential equation (SDE) and a general Ito process in terms of the local characteristics. In particular, our Ito-Alekseev-Grobner formula can be applied to derive strong approximation rates for implementable approximations of SDEs. To apply the Ito-Alekseev-Grobner formula, we need to ensure that there exists a version of the solution processes of the SDE which is twice continuously differentiable in the starting point. In the last part of this thesis, we derive conditions on the coefficient functionswhich ensure existence of solution versions." @default.
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- W2992667609 date "2019-01-01" @default.
- W2992667609 modified "2023-09-28" @default.
- W2992667609 title "On the Itô-Alekseev-Gröbner formula for stochastic differential equations" @default.
- W2992667609 doi "https://doi.org/10.17185/duepublico/70569" @default.
- W2992667609 hasPublicationYear "2019" @default.
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