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An adaptive scheme for the approximation of dissipative systems
Stochastic Process. Appl., 117 (10): 1491--1518 (2007)
DOI: 10.1016/j.spa.2007.02.004
Аннотация
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, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes 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.
