20.500.12556/RUL-161885 Pascalovi procesi in njihova karakterizacija delo diplomskega seminarja Pascal processes and their characterization Diplomska naloga spada v področje teorije verjetnosti, ki se ukvarja s slučajnimi procesi. Na začetku si bomo pogledali osnove slučajnih procesov, homogeni in nehomogeni Poissonov proces ter markovske verige, nato pa bomo predstavili tri specifične procese: Yulov proces, Poissonov proces z V randomizirano intenziteto ter standardni Pascalov proces. Cilj diplomske naloge je dokazati enako porazdeljenost teh treh procesov. To poskušamo narediti kar po definiciji za enako porazdeljene procese ter z uporabo različnih matematičnih orodij. Na koncu predstavimo algoritme za izvajanje simulacij obravnavanih slučajnih procesov. The thesis falls within the domain of probability theory, specifically focusing on stochastic processes. Initially, we will explore the fundamentals of stochastic processes, including homogeneous and non-homogeneous Poisson processes, as well as Markov chains. Subsequently, we will introduce three particular processes: the Yule process, the Poisson process with a random intensity V, and the standard Pascal process. The primary objective of this thesis is to demonstrate the equivalence in distribution of these three processes. We aim to achieve this directly from the definition for equally distributed processes and by employing a variety of mathematical tools. Finally, we present algorithms for performing simulations of the discussed stohastic processes. slučajni proces Poissonov proces markovske verige porazdelitev slučajnega procesa rojstni proces stohastic process Poisson process Markov chains distribution of a stohastic process birth process true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2024-09-15 08:16:26 2024-09-15 08:16:28 2024-09-20 10:38:00 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 143383 208298499 12906.pdf 12906.pdf 1 993C9AE48F2446439A3CCD7FA5459175 d8676534dbbde4131bf0be53c01953db55f4335c5290780b811175b81d18c1d0 f5c0d054-7329-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190874 12907.R 12907.R 1 9F17ABA6967D59F14B15E421FAAB7C88 f8262f1d04d3d6bc693b6d1b8b9c179d7f1acb33f32a6aa3390f9f1df7b2fa9a f5c11d22-7329-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190875 12908.R 12908.R 1 E09648AD026EF371C22C458CE0D6F48F 5d48f421ec97863343b6475e6291e95a89eb239385d3102538eeea9c95fac8ab f5c980a0-7329-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190876 12909.R 12909.R 1 A3683596EF22019ECCF64AFF81189408 0d5c925a4145b45e6c9bb526125863e3b3fbb35149e5aa0ff65491749d6d2767 f5c9b755-7329-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190877 12910.R 12910.R 1 731846606E48E9BADE0A7401E12DFD7A 89641404b3a856c217d4500576ecbad3c5dee19f9ed49d7463526beffcc064ad f5c9e505-7329-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=190878 Fakulteta za matematiko in fiziko 0 0 0