Generating Sparse Stochastic Processes Using Matched Splines

Leello Dadi; Shayan Aziznejad; Michael Unser

doi:10.1109/tsp.2020.3011632

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arXiv · 2008.03181

Generating Sparse Stochastic Processes Using Matched Splines

Leello Dadi·Shayan Aziznejad·Michael Unser

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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.

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BibTeX RIS

Leello Dadi, Shayan Aziznejad, Michael Unser. 2020-08-07. Generating Sparse Stochastic Processes Using Matched Splines. https://doi.org/10.1109/tsp.2020.3011632

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