Imbedded construction of stationary sequences and point processes with a random memory

DOI10.1007/BF01158695zbMath0817.60052OpenAlexW1513292917WikidataQ98839640 ScholiaQ98839640MaRDI QIDQ1339065

Laurent Massoulié, Pierre Brémaud

Publication date: 27 July 1995

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01158695

zbMATH Keywords

point processescouplingasymptotic stationarity\((A,m)\)-processesstochastic intensity kernels

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Some monotonicity and dependence properties of self-exciting point processes ⋮ Sensitivity analysis for marked Hawkes processes: application to CLO pricing ⋮ Coupling with compensators ⋮ Alternative asymptotic inference theory for a nonstationary Hawkes process ⋮ Point processes on directed linear networks ⋮ Phase transition for infinite systems of spiking neurons ⋮ Stability results for a general class of interacting point processes dynamics, and applications ⋮ Time and Palm stationarity of repairable systems

Cites Work

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• Renewal theorem for a class of stationary sequences
• On coupling of renewal processes with use of failure rates
• Ergodicity and inequalities in a class of point processes
• On coupling and weak convergence to stationarity
• An introduction to the theory of point processes
• Stochastically recursive sequences and their generalizations
• Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
• On a Representation of Random Variables

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