Affordable Access

An adaptive scheme for the approximation of dissipative systems

  • Computer Science
  • Mathematics


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.

There are no comments yet on this publication. Be the first to share your thoughts.