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| HAL: hal-00669457, version 1 |
| arXiv: 1202.2708 |
| DOI: 10.1016/j.spa.2012.04.007 |
| Detailed view |  Export this paper |
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| Stochastic Processes and their Applications 122, 7 (2012) 2553-2593 |
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| Strong and weak order in averaging for SPDEs |
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| Charles-Edouard Bréhier 1 |
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| (2012) |
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| We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of the system converges towards the solution of the averaged equation with an order of convergence is $1/2$ in a strong sense - approximation of trajectories - and $1$ in a weak sense - approximation of laws. These orders turn out to be the same as for the SDE case. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Analyse numérique, Processus stochastiques |
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| Subject | : | Mathematics/Numerical Analysis Mathematics/Probability |
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| Stochastic Partial Differential Equations – Averaging Principle – Strong and Weak Approximation |
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| hal-00669457, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00669457 | |
| oai:hal.archives-ouvertes.fr:hal-00669457 | |
| From: Maryse Collin | |
| Submitted on: Monday, 13 February 2012 11:51:39 | |
| Updated on: Monday, 4 June 2012 15:52:31 | |
