Filtering of derived point processes
type: Item
instance of: scholarly article
title: Filtering of derived point processes
zbMATH Open document ID: 0810.60042
DOI: 10.1016/0304-4149(94)90139-2
author: Günter Last
published in: Stochastic Processes and their Applications
publication date: 1995-04-04T00:00:00Z
review text: Two marked point processes on the half-line are considered: initial and derived. The derived point process is obtained from the initial one with the help of a thinning and secondary marking procedure. The conditional distribution of the initial (not observable) process till a given time with respect to the derived (observable) process till the same time is investigated. The corresponding filtering equation is derived. In the case of a semi-Markov process as the initial process the corresponding mutual conditional distribution of the last jump-time before a given time and the value just after the jump of the initial process is proved to be a solution of a Markov renewal equation.
reviewed by: B. P. Harlamov
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 519772
zbMATH Keywords: point process
zbMATH Keywords: thinning
zbMATH Keywords: filtering
zbMATH Keywords: semi-Markov process
zbMATH Keywords: Markov renewal equation
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90139-2
OpenAlex ID: W4212774181
cites work: Filtering the histories of a partially observed marked point process
cites work: Q3026011
cites work: Martingales on Jump Processes. I: Representation Results
cites work: Point processes and queues. Martingale dynamics
cites work: Markov renewal theory
cites work: Q3957682
cites work: Filtering of Markov renewal queues, IV: Flow processes in feedback queues
cites work: Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
cites work: On Bayes’ Formula for Doubly Stochastic Point Process on the Real Half-Line
cites work: Q4148534
cites work: Doubly stochastic Poisson processes and process control
cites work: State estimation for partially observed Markov chains
cites work: Filtering and detection for doubly stochastic Poisson processes
cites work: Q4714399
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description: scientific article; zbMATH DE number 519772