An adaptive scheme for the approximation of dissipative systems

Vincent Lemaire

Stochastic Processes and their Applications, 2007, vol. 117, issue 10, 1491-1518

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, 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.

Keywords: Diffusion; process; Dissipative; system; Invariant; measure; Stochastic; algorithm; Euler; method; Simulation (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (10)

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