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An adaptive scheme for the approximation of dissipative systems

Vincent Lemaire
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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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Vincent Lemaire. 2005-02-15. An adaptive scheme for the approximation of dissipative systems. https://doi.org/10.1016/j.spa.2007.02.004

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