Generating Sparse Stochastic Processes Using Matched Splines

08/07/2020

∙

by   Leello Dadi, et al.

∙

0

∙

share

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Lévy white noises. A recent paper showed that these processes are limits in law of generalized compound-Poisson processes. Based on this result, we derive an off-the-grid algorithm that generates arbitrarily close approximations of the target process. Our method relies on a B-spline representation of generalized compound-Poisson processes. We illustrate numerically the validity of our approach.