(Theoretical Project) Slowly Growing Poisson Processes
Poisson processes are used to model sparse piecewise-smooth signals. They are pure jump processes characterized by the law of the jumps and the average density of knots. The properties of the law of the jumps is intimately linked with the asymptotic behavior of the process. The goal of this project is to link the decay rate of its jumps probability with the (almost surely) inclusion of the process in the space of tempered distributions. This has recently been shown using advanced mathematical tools. Here, the aim is to find an elementary proof by studying the existence of moments of the law of jumps. The student should have a solid understanding of functional analysis and probability theory.
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