Poisson convergence for set-indexed empirical processes

DOI10.1016/S0167-7152(96)00059-4zbMath0874.60039MaRDI QIDQ1359767

B. Gail Ivanoff, Ely Merzbach

Publication date: 2 November 1997

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

empirical processPoisson processcompensatorstrong martingalesingle jump process

Mathematics Subject Classification ID

Random fields (60G60) Generalizations of martingales (60G48) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (2)

A note on Poisson approximation of rescaled set-indexed empirical processes ⋮ Some notes on poisson limits for empirical point processes

Cites Work

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• A note on the rate of Poisson approximation of empirical processes
• The space D(A) and weak convergence for set-indexed processes
• Point processes indexed by directed sets
• An extended martingale invariance principle
• Doob-Meyer decomposition for set-indexed submartingales
• Convergence of the empirical distribution to the poisson process

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