On a piece-wise deterministic Markov process model

Borovkov, K; Novikov, A

On a piece-wise deterministic Markov process model

Borovkov, K Novikov, A

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Publication Type:: Journal Article
Citation:: Statistics and Probability Letters, 2001, 53 (4), pp. 421 - 428
Issue Date:: 2001-07-01

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Field	Value	Language
dc.contributor.author	Borovkov, K	en_US
dc.contributor.author	Novikov, A https://orcid.org/0000-0001-8529-173X	en_US
dc.date.issued	2001-07-01	en_US
dc.identifier.citation	Statistics and Probability Letters, 2001, 53 (4), pp. 421 - 428	en_US
dc.identifier.issn	0167-7152	en_US
dc.identifier.uri	http://hdl.handle.net/10453/3434
dc.description.abstract	We study a piece-wise deterministic Markov process having jumps of i.i.d. sizes with a constant intensity and decaying at a constant rate (a special case of a storage process with a general release rule). Necessary and sufficient conditions for the process to be ergodic are found, its stationary distribution is found in explicit form. Further, the Laplace transform of the first crossing time of a fixed barrier by the process is shown to satisfy a Fredholm equation of second kind. Solution to this equation is given by exponentially fast converging Neumann series; convergence rate of the series is estimated. Our results can be applied to an important reliability problem. © 2001 Elsevier Science B.V.	en_US
dc.relation.ispartof	Statistics and Probability Letters	en_US
dc.relation.isbasedon	10.1016/S0167-7152(01)00074-8	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	On a piece-wise deterministic Markov process model	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	53	en_US
utslib.for	010205 Financial Mathematics	en_US
utslib.for	150201 Finance	en_US
utslib.for	010406 Stochastic Analysis and Modelling	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	53	en_US

Abstract:

We study a piece-wise deterministic Markov process having jumps of i.i.d. sizes with a constant intensity and decaying at a constant rate (a special case of a storage process with a general release rule). Necessary and sufficient conditions for the process to be ergodic are found, its stationary distribution is found in explicit form. Further, the Laplace transform of the first crossing time of a fixed barrier by the process is shown to satisfy a Fredholm equation of second kind. Solution to this equation is given by exponentially fast converging Neumann series; convergence rate of the series is estimated. Our results can be applied to an important reliability problem. © 2001 Elsevier Science B.V.

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http://hdl.handle.net/10453/3434