Gaussian and Sparse Processes Are Limits of Generalized Poisson\n Processes

2017/02/16 by Julien Fageot, Virginie Uhlmann, Fageot, Julien +3
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Image and Signal Denoising Methods #Information Theory (cs.IT) #Probability (math.PR) #Statistical and numerical algorithms #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1702.05003

openalex publication_date 2017/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of sparse stochastic processes offers a broad class of statistical\nmodels to study signals. In this framework, signals are represented as\nrealizations of random processes that are solution of linear stochastic\ndifferential equations driven by white L 'evy noises. Among these processes,\ngeneralized Poisson processes based on compound-Poisson noises admit an\ninterpretation as random L-splines with random knots and weights. We\ndemonstrate that every generalized L 'evy process-from Gaussian to sparse-can\nbe understood as the limit in law of a sequence of generalized Poisson\nprocesses. This enables a new conceptual understanding of sparse processes and\nsuggests simple algorithms for the numerical generation of such objects.\n

Citations

• Fractional Brownian Motions, Fractional Noises and Applications
• The Fractal Geometry of Nature

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