An adaptive scheme for the approximation of dissipative systems
By Vincent Lemaire. 2005
50 citations recorded by the source corpus.
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.
Subfields: Finance, Modeling and Simulation, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ea10b09ff6f65099d7909f2bb9b44dd948b391cc
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Citations in the corpus
- Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2009, unknown): “A completely different adaptive time-stepping algorithm with focus on long time approximation is proposed by Lemaire (2007).”
- Stochastic Heavy ball (2016, background): “g [Lem07] for instance in a diffusion setting).”
- Recursive computation of the invariant measure of a stochastic differential equation driven by a Lévy process (2005, background): “for every continuous function f with polynomial growth (see [14, 15] for more details and [17] for extensions).”
- Adaptive Euler–Maruyama method for SDEs with nonglobally Lipschitz drift (2016, unknown): “the accuracy of numerical approximations, see [4, 11, 15, 16, 17, 18, 24, 28] and the references therein.”