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

Direct link
Large Deviations on Longest Runs
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2016 (English)Student paper other, 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The study on the longest stretch of consecutive successes in \random" trials dates back to 1916 when the German philosopher Karl Marbe wrote a paper concerning the longest stretch of consecutive births of children of the same sex as appearing in the birth register of a Bavarian town. The result was actually used by parents to \predict" the sex of their children. The longest stretch of same-sex births during that time in 200 thousand birth registrations was actually 17 t log2(200 103): During the past century, the research of longest stretch of consecutive successes (longest runs) has found applications in various areas, especially in the theory of reliability. The aim of this thesis is to study large deviations on longest runs in the setting of Markov chains. More precisely, we establish a general large deviation principle for the longest success run in a two-state (success or failure) Markov chain. Our tool is based on a recent result regarding a general large deviation for the longest success run in Bernoulli trails. It turns out that the main ingredient in the proof is to implement several global and local estimates of the cumulative distribution function of the longest success run.

Place, publisher, year, edition, pages
2016. , 29 p.
Keyword [en]
Large deviation principle, Markov chain, Reliability theory, K-out-of-n system.
National Category
Natural Sciences Mathematics
URN: urn:nbn:se:liu:diva-128822ISRN: LiTH-MAT-INT-G--2016/01--SEOAI: diva2:932252
Subject / course
Available from: 2016-06-01 Created: 2016-06-01 Last updated: 2016-06-01Bibliographically approved

Open Access in DiVA

Large Deviations on Longest Runs(312 kB)35 downloads
File information
File name FULLTEXT01.pdfFile size 312 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Zhu, Yurong
By organisation
Mathematical Statistics Faculty of Science & Engineering
Natural SciencesMathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 35 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 100 hits
ReferencesLink to record
Permanent link

Direct link