liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Strong memoryless times and rare events in Markov renewal point processes
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
2004 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 32, no 3B, 2446-2462 p.Article in journal (Refereed) Published
Abstract [en]

Let $W$ be the number of points in $(0,t]$ of a stationary finite-state Markov ren ewal point process. We derive a bound for the total variation distance between the distribution of $W$ and a compound Poisson distribution. For any nonnegative rand om variable $\zeta$ we construct a ``strong memoryless time'' $\hat\zeta$ such tha t $\zeta-t$ is exponentially distributed conditional on $\{\hat\zeta\leq t,\zeta>t \}$, for each $t$. This is used to embed the Markov renewal point process into ano ther such process whose state space contains a frequently observed state which rep resents loss of memory in the original process. We then write $W$ as the accumulat ed reward of an embedded renewal reward process, and use a compound Poisson approx imation error bound for this quantity by Erhardsson. For a renewal process, the bo und depends in a simple way on the first two moments of the interrenewal time dist ribution, and on two constants obtained from the Radon-Nikodym derivative of the i nterrenewal time distribution with respect to an exponential distribution. For a Poisson process, the bound is 0.

Place, publisher, year, edition, pages
2004. Vol. 32, no 3B, 2446-2462 p.
Keyword [en]
Strong memoryless time, Markov renewal process, number of points, rare event, compound Poisson, approximation, error bound
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-23156DOI: 10.1214009117904000000054Local ID: 2560OAI: oai:DiVA.org:liu-23156DiVA: diva2:243470
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2011-01-12

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Erhardsson, Torkel

Search in DiVA

By author/editor
Erhardsson, Torkel
By organisation
The Institute of TechnologyMathematical Statistics
In the same journal
Annals of Probability
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 350 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf