Equivalence of functional limit theorems for stationary point processes and their Palm distributions

DOI10.1007/BF00367306zbMath0671.60025MaRDI QIDQ1119261

Gert Nieuwenhuis

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Palm distributionmixingstationary point processtheoremsfunctional limitweak convergence independent of a \(\sigma\)-field

Mathematics Subject Classification ID

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

Related Items (12)

On time- and cycle-stationarity ⋮ CONDITIONS FOR THE PROPAGATION OF MEMORY PARAMETER FROM DURATIONS TO COUNTS AND REALIZED VOLATILITY ⋮ Bridging the gap between a stationary point process and its Palm distribution ⋮ Heavy-Traffic Limit of the GI/GI/1 Stationary Departure Process and Its Variance Function ⋮ Minimizing the Maximum Expected Waiting Time in a Periodic Single-Server Queue with a Service-Rate Control ⋮ Asymptotic mean stationarity and absolute continuity of point process distributions ⋮ Extending the FCLT version of \(L=\lambda W\) ⋮ A Rare-Event Simulation Algorithm for Periodic Single-Server Queues ⋮ Heavy-traffic limits for nearly deterministic queues: Stationary distributions ⋮ Stationary partitions and Palm probabilities ⋮ Marked point processes in discrete time ⋮ Modeling and forecasting persistent financial durations

Cites Work

• Central limit theorems for point processes
• On mixing sequences of sets
• Some Useful Functions for Functional Limit Theorems
• An invariance principle for the law of the iterated logarithm
• Functional central limit theorems for processes with positive drift and their inverses
• Weak convergence of probability measures and random functions in the function space D[0,∞)
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