Coupling with compensators
type: Item
instance of: scholarly article
title: Coupling with compensators
zbMATH Open document ID: 0889.60047
DOI: 10.1016/S0304-4149(96)00110-X
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: Two general methods for coupling marked point processes (MPPs) on the real half-line are proposed. The MPPs are explicitly formulated in terms of (canonical) compensators, i.e. there is a (predictable in the canonical sense) kernel \(\alpha \) from \(S\times N_{\mathcal {X}}\) to \(R^{+} \times \mathcal {X}\), where \(S\) is the space of initial values, \(N_{\mathcal {X}}\) is the set of all possible realizations of the MPP with the mark space \(\mathcal {X}\). Coupling is a device used to establish convergence of stochastic processes. The main aim of the present paper is to prove the following property of ``weak ergodicity'': the total variance distance between time-shifted processes with the same compensator (but possibly different initial conditions) tends to zero.
reviewed by: Martin Janžura
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1134794
zbMATH Keywords: coupling
zbMATH Keywords: marked point process
zbMATH Keywords: compensator
zbMATH Keywords: weak ergodicity
author: Günter Last
MaRDI profile type: Publication
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full work available at URL: s0304-4149(96)00110-x
OpenAlex ID: W4213353050
description: scientific article; zbMATH DE number 1134794