Abstract
This chapter is devoted to the notions which constitute the foundation of our inquiry. They are presented briefly together with references allowing a deeper investigation. Poisson random measures are random distributions of points in abstract spaces widely used in applications in order to represent spatial independence (see for instance references in Neveu Processus Ponctuels, 1997, [270]). Lévy processes i.e. processes with independent increments, may be defined through Poisson random measures so that equipping Poisson random measures with Dirichlet forms make this tool available for studying Lévy functionals . Next we present the framework adopted in the book and the famous chaos decomposition of the \(L^2\) space of Poisson random measures.
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© 2015 Springer International Publishing Switzerland
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Bouleau, N., Denis, L. (2015). Reminders on Poisson Random Measures. In: Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes. Probability Theory and Stochastic Modelling, vol 76. Springer, Cham. https://doi.org/10.1007/978-3-319-25820-1_3
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DOI: https://doi.org/10.1007/978-3-319-25820-1_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-25820-1
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