On convergence in variation of the distributions of multivariate point processes

DOI10.1007/BF00533721zbMath0532.60042OpenAlexW1971408856MaRDI QIDQ3314665

Youri M.Kabanov, Robert Sh. Liptser

Publication date: 1983

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00533721

zbMATH Keywords

marked point processconvergence in variationcompensators

Mathematics Subject Classification ID

Convergence of probability measures (60B10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Limit theorems in probability theory (60F99)

Related Items (7)

Point processes in fast Jackson networks ⋮ Poisson approximations for Markov-driven point processes ⋮ Coupling with compensators ⋮ Fatou's Lemma in Its Classical Form and Lebesgue's Convergence Theorems for Varying Measures with Applications to Markov Decision Processes ⋮ Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process ⋮ On the variation distance for probability measures defined on a filtered space ⋮ Poisson approximation

Cites Work

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• Calcul stochastique et problèmes de martingales
• A martingale approach to the Poisson convergence of simple point processes
• Some limit theorems for simple point processes (a martingale approach)
• Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales

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