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Spatial Poisson Processes

  • Nicolas Privault
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

Spatial Poisson process are typically used to model the random scattering of configuration points within a plane or a three-dimensional space X. In case \(X = \mathbb{R}_{+}\) is the real half line, these random points can be identified with the jump times (T k ) k≥1 of the standard Poisson process \((N_{t})_{t\in \mathbb{R}_{+}}\) introduced in Section  10.1. However, in contrast with the previous chapter, no time ordering is a priori imposed here on the index set X. Sections 12.4 and 12.5 contain some more advanced results on moments and deviation inequalities for Poisson stochastic integrals.

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Copyright information

© Springer Science+Business Media Singapore 2013

Authors and Affiliations

  • Nicolas Privault
    • 1
  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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