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Martingale methods for the analysis of waiting times for patterns

Maciej Zbigniew Falkowski

Abstract

The thesis deals with a martingale method (the so called gambling teams method of Kulldorff and Pozdnyakov) of computing the expected waiting times for patterns in sequences of independent and identically distributed random variables. We present the theory developed by the Kulldorff and Pozdnyakov, and find numerous examples of applications of the method.
Diploma type
Engineer's / Bachelor of Science
Diploma type
Bachelor thesis
Author
Maciej Zbigniew Falkowski (FMIS) Maciej Zbigniew Falkowski,, Faculty of Mathematics and Information Science (FMIS)
Title in Polish
Metody martyngałowe badania czasów oczekiwania na wzorce
Supervisor
Wojciech Matysiak (FMIS/DPMS) Wojciech Matysiak,, Department of Probability and Mathematical Statistics (FMIS/DPMS)Faculty of Mathematics and Information Science (FMIS)
Certifying unit
Faculty of Mathematics and Information Science (FMIS)
Affiliation unit
Department of Probability and Mathematical Statistics (FMIS/DPMS)
Study subject / specialization
, Matematyka
Language
(pl) Polish
Status
Finished
Defense Date
09-10-2019
Issue date (year)
2019
Reviewers
Wojciech Matysiak (FMIS/DPMS) Wojciech Matysiak,, Department of Probability and Mathematical Statistics (FMIS/DPMS)Faculty of Mathematics and Information Science (FMIS) Ewa Anna Frankiewicz (FMIS/DAST) Ewa Anna Frankiewicz,, Department of Analysis and Sigularity Theory (FMIS/DAST)Faculty of Mathematics and Information Science (FMIS)
Keywords in Polish
wzorzec, czas oczekiwania, martyngał, funkcja tworząca
Keywords in English
pattern, waiting time, martingale, generating function
Abstract in Polish
W pracy przedstawiono pewną metodę martyngałową (tzw. metodę zespołów hazardowych pochodzącą od Kulldorffa i Pozdnyakova) badania średnich czasów oczekiwania na wzorce w ciągach niezależnych zmiennych losowych. Opisano zarówno teorię pochodzącą z literatury przedmiotu, jak i wiele autorskich przykładów jej zastosowań.
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    metody_martyngalowe_lic.pdf
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Local fields
Identyfikator pracy APD: 36060

Uniform Resource Identifier
https://repo.pw.edu.pl/info/bachelor/WUT54977bcded2c48e0a08828c70396348c/
URN
urn:pw-repo:WUT54977bcded2c48e0a08828c70396348c

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