Generating Sparse Stochastic Processes Using Matched Splines
Statistics Theory
2020-08-10 v1 Statistics Theory
Abstract
We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by L\'evy 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.
Cite
@article{arxiv.2008.03181,
title = {Generating Sparse Stochastic Processes Using Matched Splines},
author = {Leello Dadi and Shayan Aziznejad and Michael Unser},
journal= {arXiv preprint arXiv:2008.03181},
year = {2020}
}