Vejitveni procesi

diplomsko delo

Mojca Borin (Author), Dominik Benkovič (Mentor)

Abstract

Vejitveni proces je matematični model razvoja in rasti neke populacije. Opazujemo lahko razvoj populacije po generacijah ali pa po časovnih intervalih. Takim vejitvenim procesom pravimo časovno odvisni. Obravnavali smo jih s pomočjo rodovne funkcije in s pomočjo markovskih verig. Najprej so razloženi osnovni pojmi, kot so neodvisne naključne spremenljivke, rodovna funkcija in markovske verige, ki so potrebni za razumevanje teorije o vejitvenih procesih. Pri tem gre predvsem za izračun verjetnosti izumrtja populacije. Ob teoretični obravnavi izumrtja je na konkretnih primerih predstavljen vejitveni proces z začetno geometrijsko porazdelitvijo, za katerega je narejena tudi računalniška simulacija. Program je narejen v programskem jeziku C in vejitveni proces simulira z gradnjo drevesa in izračunom verjetnosti izumrtja. Simulacija da rezultate, ki so primerljivi s teoretično izračunanimi.

Keywords

matematika;vejitveni procesi;čas;rodovna funkcija;markovska veriga;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:	[M. Kramer]
UDC:	51(043.2)
COBISS:	17314568
Views:	1858
Downloads:	81
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	BRANCHING PROCESSES
Secondary abstract:	The branching process is a mathematical model of development and growth of a population. We can suppose that a population evolves in generations or we attach another random variable, called "age". We name them age-dependent branching processes. For describing such processes we use probability generating functions and Markov chains. At first are explained basic concepts, such as dicrete random variables, probability generating functions and markov chains, which are necessary to understand the theory of branching processes. Especially we are interested in expressing probability of ultimate extinction. In addition to the theoretical treatment of extinction, are also exemples which presents the geometrical distributed processes. Those are included in computer simulation. The program, designed in C , simulate growth of a population with family tree of a branching process and calculate the probability of extinction. Results of the simulation are comparable to the theoretical results.
Secondary keywords:	branching process;age-dependent branching process;probability gen- erating function;markov chain;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	51 f., [3] f. pril.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18228