20.500.12556/DKUM-11725 LASTNE VREDNOSTI IN NEHOMOGENE MARKOVSKE VERIGE EINGENVALUES AND NONHOMOGENEOUS MARKOV CHAINS Diplomska naloga govori predvsem o homogenih markovskih verigah in njihovi konvergenci k stacionarni porazdelitvi. V začetnem poglavju je omenjenih nekaj nazornih primerov uporabe in osnovne informacije o homogenih markovskih verigah, kot so stohastični procesi, matrike prehoda, različna stanja, stacionarna porazdelite, ergodičnost,.... Sledijo definicije in uporabni rezultati s področja lastnih vrednosti in lastnih vektorjev. Uvodni del pa zaključuje pomemben izrek o konvergenci k stacionarni porazdelitvi homogene markovske verige. V nadaljevanju sledi formulacija Perron-Frobeniusovega izreka, uporaba lastne strukture matrike prehoda ergodične homogene markovske verige v končnem prostoru stanj pri določanju hitrosti konvergence k stacionarni porazdelitvi, ki pa je enaka po absolutni vrednosti drugi največji lastni vrednosti in nekateri načini določanja njene spodnje in zgornje meje. V zadnjem poglavju pa se soočimo s kompleksnejšim konceptom, in sicer nehomogenimi markovskimi verigami in pogoji za določitev krepke in šibke ergodičnosti. This paper presents homogeneous Markov chains and their convergence to steady state. In initial chapter are written a few evidental examples of use homogeneous Markov chain and given some basic informations about homogeneous Markov chain, for example stochastic process, transition matrix, diversity states, stationary distribution, ergodicity,... The definitions and useful results of eigevaleus and eigevectors are discribed in following chapter. Introduction part of this paper is concluded with an important theorem of convergence to stady state. In following text we can find formulation of Perron-Frobenius theorem, way of use eigenstructure transition matrix ergodic finite state space homogeneous Markov chain to define relative speed to stationary distribution. The relative speed to stationary distribution is equal to the secondlargest eigenvalue modulus. In continuing text there are decribed some ways of defining lower and upper bound of second-largest eigenvalue modulus. In final chapter we confront with complex concept, with nonhomogeneous markov chains and conditions to define strong and weak ergodicity of nonhomogeneous Markov chains. Homogene markovske verige nehomogene markovske verige Perron-Frobeniusov izrek stacionarna porazdelitev ergodičnost. Homogeneous markov chain nonhomogeneous markov chain Perron-Frobenius theorem stationary distribution ergodicity. true true false [J. Karo] Slovenski jezik Angleški jezik Diplomsko delo 2009-09-14 13:30:23 2009-11-17 13:47:22 2022-04-12 00:08:23 2022-04-18 03:25:01 2009 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51 17183752 URN:SI:UM:DK:PPA53WLP UNI_Karo_Janja_2009.pdf UNI_Karo_Janja_2009.pdf 1 99AC4BE09116651C73E68936536649E6 7de25407f82ec69c20dbb0c1c885ed81f1e87255e50377ef14b574168db1fa1e 34f073b0-7c03-11eb-bb7a-00155d0001ca 20.500.12556/dkum/8959a84f-1599-47cc-8a39-2cdd44998c2b https://dk.um.si/Dokument.php?lang=slv&id=10623 Fakulteta za naravoslovje in matematiko 0 0 0