On the Itô-Alekseev-Gröbner formula for stochastic differential equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866914849414447104 |
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| author | Hudde, Anselm Hutzenthaler, Martin Jentzen, Arnulf Mazzonetto, Sara |
| author_facet | Hudde, Anselm Hutzenthaler, Martin Jentzen, Arnulf Mazzonetto, Sara |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1812_09857 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the Itô-Alekseev-Gröbner formula for stochastic differential equations Hudde, Anselm Hutzenthaler, Martin Jentzen, Arnulf Mazzonetto, Sara Probability 60H10 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. |
| title | On the Itô-Alekseev-Gröbner formula for stochastic differential equations |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/1812.09857 |