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master's thesis
Markovljevi lanci u neprekidnom vremenu i vremena čekanja
2022. urn:nbn:hr:126:425344
Petrović, Ivana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Petrović, I. (2022). Markovljevi lanci u neprekidnom vremenu i vremena čekanja (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:425344

Petrović, Ivana. "Markovljevi lanci u neprekidnom vremenu i vremena čekanja." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:425344

Petrović, Ivana. "Markovljevi lanci u neprekidnom vremenu i vremena čekanja." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:425344

Petrović, I. (2022). 'Markovljevi lanci u neprekidnom vremenu i vremena čekanja', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:425344

Petrović I. Markovljevi lanci u neprekidnom vremenu i vremena čekanja [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:425344

I. Petrović, "Markovljevi lanci u neprekidnom vremenu i vremena čekanja", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:425344

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Metadata
TitleMarkovljevi lanci u neprekidnom vremenu i vremena čekanja
Title (english)Continuous-Time Markov Chains and Waiting Times
AuthorIvana Petrović
MentorIvan Papić (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberIvan Papić (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-05-12, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom radu upoznajemo se s Markovljevim lancima u neprekidnom vremenu, pripadnim vremenima skokova i vremenima čekanja. Osim toga, radimo konstrukciju Markovljevog lanca, definiramo pripadne prijelazne vjerojatnosti i generatorsku matricu. Zatim iskazujemo jednadžbe unatrag i unaprijed. Na kraju drugog poglavlja radimo klasifikaciju stanja lanca, definiramo invarijantnu i graničnu distribuciju te ih povezujemo teoremom. Nakon toga, prezentiramo primjere Markovljevih lanaca u neprekidnom vremenu. Detaljnije se bavimo procesom radanja i umiranja te Poissonovim procesom. Naposljetku ilustriramo teoriju na nekoliko modela redova čekanja, model infekcije te model rasta s imigracijom.
Abstract (english)
In this paper we introduce continuous-time Markov chains, the corresponding jumping and waiting times. Moreover, we construct the Markov chain, introduce transient probabilities and the generator matrix. Next, we state the backward and forward equation. At the end of section two, we go through the classification of states of the chain, define the invariant and stationary distribution, and connect them by a theorem. Finally, we present some examples of continuous-time Markov chains. We thoroughly go into birth and death process and Poisson process. Lastly, we illustrate the theory in modeling queues, infection model and immigration growth model.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:425344
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-05-16 07:17:07