Article

# An adaptive scheme for the approximation of dissipative systems

(Impact Factor: 1.05). 03/2005; DOI: 10.1016/j.spa.2007.02.004
Source: arXiv

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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