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2013S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture

## Aim of course

Ability to create and analyze stochastic models ,

deepening in the field of mathematical probability

## Subject of course

multivariate limit distribution rate, symmetric distributions,
Zero-one law, dependences of multivariate distributions and characterisations

characteristic functions, Levy'scher continuity theorem, three-series theorem,
infinitely divisible distributions and Levy-Khinchin formula, stable distributions,
Poisson point process

convergencies of measures
vague convergence, portmanteau theorem, theorem of Slutsky,
Tightness, Theorem  of Prohorov, select theorem of Helly,

Product spaces (infinite dimensional) projective family, semi-Markov kernels and groups, Kolmogorov' extension
Interchangeability, theorem of Definetti,

Markov chains, invariant measures, convergence theorem for Markov chains, Monte Carlo method ,ergodic theorems
mixing systems,

Martingales, stopping times, discrete stochastic integral Martingaldarstellungssatz, Doob decomposition,
optional sampling and optional stopping, Martingalkonvergenzsätze,
Rückwärtsmartingale

Laws of the iterated logarithm, Skorohod'sche embedding theorem, theorem of Hartman and Wintner,

Unterlagen auf der Homepage verfügbar

## Course dates

DayTimeDateLocationDescription
Wed16:00 - 17:3006.03.2013 - 26.06.2013Seminarraum 107/1 SC Probability Theory 2
Tue11:00 - 13:0019.03.2013 - 25.06.2013Sem.R. DA grün 06A SC Probability Theory
Fri12:00 - 15:0022.03.2013Sem.R. DA grün 06A ET1
Fri12:00 - 15:0019.04.2013Sem.R. DA grün 06A ET2
Fri12:00 - 15:0003.05.2013Sem.R. DA grün 06A WT3
selected chapters of probability theory - Single appointments
DayDateTimeLocationDescription
Wed06.03.201316:00 - 17:30Seminarraum 107/1 SC Probability Theory 2
Wed13.03.201316:00 - 17:30Seminarraum 107/1 SC Probability Theory 2
Tue19.03.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Fri22.03.201312:00 - 15:00Sem.R. DA grün 06A ET1
Tue09.04.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue16.04.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Fri19.04.201312:00 - 15:00Sem.R. DA grün 06A ET2
Tue23.04.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue30.04.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Fri03.05.201312:00 - 15:00Sem.R. DA grün 06A WT3
Tue07.05.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue14.05.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue28.05.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue04.06.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue11.06.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue18.06.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Tue25.06.201311:00 - 13:00Sem.R. DA grün 06A SC Probability Theory
Wed26.06.201316:00 - 17:30Seminarraum 107/1 SC Probability Theory 2

Not necessary

## Literature

Books (recommended)

H. Bauer  - Wahrscheinlichkeitstheorie  -  de Gruyter
P. Billingsley - Probability and Measure - Wiley
P. Billingsley - Convergence of Probability Measures - Wiley
R. M. Dudley - Real Analysis and Probability - Cambridge University Press
B. Gnedenko -  Theory of Probability - Gordon and Breach Science Publishers/AMS Chelsey Pub.
S. Karlin & H.  Taylor - A first course in stochastic processes - Academic Press
S. Karlin & H.  Taylor - A second course in stochastic processes - Academic Press
A. Klenke - Wahrscheinlichkeitstheorie - Springer
N. Kusolitsch - Maß- und Wahrscheinlichkeitstheorie  - Springer
S. Ross - Introduction to. Probability Models - Academic Press
A. Shiryaev Probability - Springer
K. Schürger - Wahrscheinlichkeitstheorie - Oldenbourg

## Previous knowledge

Maß- & Wahrscheinlichkeitstheorie (I & II)  (besonders UE) empfohlen

German