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Erschienen in:
2013 | OriginalPaper | Buchkapitel
12. Spatial Poisson Processes
verfasst von : Nicolas Privault
Erschienen in: Understanding Markov Chains
Verlag: Springer Singapore
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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.