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Generating Sparse Stochastic Processes Using Matched Splines

L. Dadi, S. Aziznejad, M. Unser

IEEE Transactions on Signal Processing, vol. 68, pp. 4397-4406, July 24, 2020.



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.


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