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An adaptive scheme for the approximation of dissipative systems

Abstract : We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, regular explicit Euler scheme --with constant or decreasing step-- may explode and implicit Euler scheme are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.
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Contributor : Vincent Lemaire <>
Submitted on : Tuesday, February 15, 2005 - 5:12:28 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
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Vincent Lemaire. An adaptive scheme for the approximation of dissipative systems. Stochastic Processes and their Applications, Elsevier, 2007, 117 (10), pp.1491-1518. ⟨10.1016/j.spa.2007.02.004⟩. ⟨hal-00004266⟩

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