Laplace transform identities for the volume of stopping sets based on Poisson point processes

DOI10.1239/aap/1449859794zbMath1366.60075OpenAlexW2210640021MaRDI QIDQ2786420

Nicolas Privault

Publication date: 12 February 2016

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aap/1449859794

zbMATH Keywords

gamma-type distributionPoisson point processstopping setanticipating stochastic calculusGirsanov identity

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Generalizations of martingales (60G48) Stopping times; optimal stopping problems; gambling theory (60G40) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (3)

Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees ⋮ Cardinality estimation for random stopping sets based on Poisson point processes ⋮ Invariance of Poisson point processes by moment identities with statistical applications

Cites Work

• Unnamed Item
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• The optional sampling theorem for martingales indexed by directed sets
• On the homogeneous planar Poisson point process
• Stochastic and Integral Geometry
• Gamma distributions for stationary Poisson flat processes
• Decomposition of gamma-distributed domains constructed from Poisson point processes
• Stopping sets: Gamma-type results and hitting properties
• Gamma-type results and other related properties of Poisson processes
• Moments of Poisson stochastic integrals with random integrands
• A more comprehensive complementary theorem for the analysis of Poisson point processes
• Strong Markov Property of Poisson Processes and Slivnyak Formula
• Theory of Random Sets

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