Proces kitajske restavracije : delo diplomskega seminarja

Vavtar, Oskar (author), Bernik, Janez (mentor)

Proces kitajske restavracije je slučajni proces v diskretnem času, indeksiran z množico naravnih števil, katerega realizacijo ob vsakem času lahko interpretiramo kot particijo. Njegovo konstrukcijo motivira teorija neskončnih izmenljivih particij ter njej sorodna teorija slučajnih diskretnih verjetnostnih mer - izkaže se namreč, da ima proces kitajske restavracije mnogo lepih lastnosti, ki bi si jih v določenih situacijah želeli. V delu predstavimo teoretično ozadje in izvedemo nekaj simulacij tega procesa.

• Language: Slovenian
• Keywords: slučajni procesi, slučajne izmenljive particije, slučajne diskretne verjetnostne mere
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2022
• PID: 20.500.12556/RUL-139117
• UDC: 519.2
• COBISS.SI-ID: 120012547
• Publication date in RUL: 31.08.2022

Secondary language

• Language: English
• Title: Chinese restaurant process

Abstract

Chinese restaurant process is a discrete-time stochastic process, indexed with the set of natural numbers, whose realization at each time can be interpreted as a partition. Its construction is motivated by the theory of infinite exchangeable random partitions and the related theory of random discrete probability measures - Chinese restaurant process happens to possess some nice properties, desirable in certain situations. This work includes both the treatment of theoretical background as well as some simulations of said process.

• Keywords: stochastic processes, random exchangeable partition, random discrete probability measures