Lastne vrednosti in nehomogene markovske verige

diplomsko delo

Janja Karo (Author), Dominik Benkovič (Mentor)

Abstract

Diplomsko delo 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 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.

Keywords

matematika;markovske verige;ergodičnost;porazdelitve;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2009
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[J. Karo]
UDC:	51
COBISS:	17183752
Views:	2724
Downloads:	310
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	EINGENVALUES AND NONHOMOGENEOUS MARKOV CHAINS
Secondary abstract:	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.
Secondary keywords:	Homogeneous markov chain;nonhomogeneous markov chain;Perron-Frobenius theorem;stationary distribution;ergodicity.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 61 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18089