Explicit domain preserving numerical schemes for a class of stochastic differential equations
Charles-Edouard Bréhier, David Cohen
Source abstract
We construct and analyze numerical schemes for systems of stochastic differential equations, which preserve almost surely a given hypercube of arbitrary dimension. We propose a new general class of explicit schemes, such that for any choice of the time-step size the numerical solution takes values in the hypercube. We prove strong and weak convergence results for this general class of domain preserving numerical schemes, with strong order $1/2$ and weak order $1$ in general. We also construct a variant of the scheme which achieves strong order $1$ when the stochastic differential equation is driven by a one-dimensional Brownian motion. The convergence results are illustrated with numerical experiments.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.