Stochastic B-series and order conditions for exponential integrators

Alemayehu Adugna Arara; Kristian Debrabant; Anne Kværnø

doi:10.1007/978-3-319-96415-7_37

Stochastic B-series and order conditions for exponential integrators

Alemayehu Adugna Arara, Kristian Debrabant, Anne Kværnø

Department of Mathematics and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both Itô and Stratonovich integration.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications : ENUMATH 2017
Editors	Florin Adrian Radu, Kundan Kumar, Inga Berre, Jan Martin Nordbotten, Iuliu Sorin Pop
Publisher	Springer
Publication date	5. Jan 2019
Pages	419-427
ISBN (Print)	978-3-319-96414-0
ISBN (Electronic)	978-3-319-96415-7
DOIs	https://doi.org/10.1007/978-3-319-96415-7_37
Publication status	Published - 5. Jan 2019
Event	European Conference on Numerical Mathematics and Advanced Applications - University of Bergen, Voss, Norway Duration: 25. Sept 2017 → 29. Sept 2017 http://www.uib.no/en/enumath2017

Conference

Conference	European Conference on Numerical Mathematics and Advanced Applications
Location	University of Bergen
Country/Territory	Norway
City	Voss
Period	25/09/2017 → 29/09/2017
Internet address	http://www.uib.no/en/enumath2017

Series	Lecture Notes in Computational Science and Engineering
Volume	126
ISSN	1439-7358

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10.1007/978-3-319-96415-7_37

Stochastic B-series and order conditions for exponential integratorsSubmitted manuscript, 874 KB

https://arxiv.org/pdf/1801.02051.pdf

Cite this

Arara, Alemayehu Adugna ; Debrabant, Kristian ; Kværnø, Anne. / Stochastic B-series and order conditions for exponential integrators. Numerical Mathematics and Advanced Applications: ENUMATH 2017. editor / Florin Adrian Radu ; Kundan Kumar ; Inga Berre ; Jan Martin Nordbotten ; Iuliu Sorin Pop. Springer, 2019. pp. 419-427 (Lecture Notes in Computational Science and Engineering, Vol. 126).

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abstract = "We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both It{\^o} and Stratonovich integration.",

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Arara, AA, Debrabant, K & Kværnø, A 2019, Stochastic B-series and order conditions for exponential integrators. in FA Radu, K Kumar, I Berre, JM Nordbotten & IS Pop (eds), Numerical Mathematics and Advanced Applications: ENUMATH 2017. Springer, Lecture Notes in Computational Science and Engineering, vol. 126, pp. 419-427, European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway, 25/09/2017. https://doi.org/10.1007/978-3-319-96415-7_37

Stochastic B-series and order conditions for exponential integrators. / Arara, Alemayehu Adugna; Debrabant, Kristian; Kværnø, Anne.
Numerical Mathematics and Advanced Applications: ENUMATH 2017. ed. / Florin Adrian Radu; Kundan Kumar; Inga Berre; Jan Martin Nordbotten; Iuliu Sorin Pop. Springer, 2019. p. 419-427 (Lecture Notes in Computational Science and Engineering, Vol. 126).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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AU - Kværnø, Anne

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AB - We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both Itô and Stratonovich integration.

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T2 - European Conference on Numerical Mathematics and Advanced Applications

Y2 - 25 September 2017 through 29 September 2017

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Stochastic B-series and order conditions for exponential integrators

Abstract

Conference

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