State space splitting of a finite markov process and some discussions on related counting processes

Lirong Cui, He Yi and Narayanaswamy Balakrishnan

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 11, 4021-4052

Abstract: In this paper, state space of a time-homogeneous Markov process is split into several ordered subspaces. Then, there are three kinds of transitions between states—transitions from a higher-order subspace to a lower-order subspace, transitions within the same subspace, and transitions from a lower-order subspace to a higher-order subspace. Considering time interval omission problem and first passage time considered, we define some related counting processes for the Markov process and discuss their associated probabilities, expectations and generating functions by using Laplace transform. The main results are presented in matrix forms. The relationships among counting processes and their special cases are also discussed briefly. Some simple numerical examples are presented to illustrate the established results. These results will be useful in different problems arising in reliability, economics and social science fields.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2021.1986531 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:52:y:2023:i:11:p:4021-4052

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2021.1986531

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().