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Title

Drift-preserving numerical integrators for stochastic Poisson systems

Authors
Cohen, David
Year 2020
Description 15
Abstract We perform a numerical analysis of randomly perturbed Poisson systems. For the considered Itô perturbation of Poisson differential equations, we show the longtime behavior of the energy and quadratic Casimirs for the exact solution. We then propose and analyze a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence one, weak order of convergence two. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.
Keywords Stochastic differential equationsStochastic Hamiltonian systemsStochastic Poisson systemsEnergyCasimirTrace formulaNumerical schemesStrong convergenceWeak convergence
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Research group Analyse numérique
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COHEN, David, VILMART, Gilles. Drift-preserving numerical integrators for stochastic Poisson systems. 2020. https://archive-ouverte.unige.ch/unige:136314

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Deposited on : 2020-06-02

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