Probability theory II
General data
Course ID: | 1000-115aRP2a |
Erasmus code / ISCED: |
11.103
|
Course title: | Probability theory II |
Name in Polish: | Rachunek prawdopodobieństwa II (potok I) |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Obligatory courses for 4th grade JSIM (3I+4M) |
ECTS credit allocation (and other scores): |
(not available)
|
Language: | Polish |
Type of course: | obligatory courses |
Prerequisites: | Probability theory I 1000-114aRP1a |
Short description: |
The course contains an introduction to the convergence theory for probability distributions (equivalence of various definitions, Central Limit Theorem) and to applications of harmonical analysis in the theory (properties of characteristic functions). Moreover, some elements of martingale theory and Markov chains will be discussed. |
Full description: |
Convergence of probability distributions. The characteristic function of a probability distribution, applications to computing moments and distributions of sums of independent random variables. The uniqueness theorem. Levy's theorem stating that the convergence of probability distributions can be described in terms of the pointwise convergence of their characteristic functions. The Central Limit Theorem. Introduction to the theory of martingales ("fair games"). Stopping moments. Doob's "optional sampling" theorem. Markov chains, ergodicity. |
Bibliography: |
(in Polish) J. Jakubowski i R. Sztencel, Wstęp do teorii prawdopodobieństwa, SCRIPT, Warszawa 2001. P. Billingsley, Prawdopodobieństwo i miara, PWN, Warszawa 1987. W. Feller, Wstęp do rachunku prawdopodobieństwa (t. I i II), PWN, Warszawa 1975 i późniejsze wydania. A. Borowkow, Rachunek prawdopodobieństwa, PWN, Warszawa 1975. S. Zubrzycki, Wykłady z rachunku prawdopodobieństwa i statystyki matematycznej, PWN, Warszawa 1970. A. Sziriajew, Wierojatnost, Nauka, Moskwa 1980. |
Copyright by University of Warsaw.