401-3601-00L  Probability Theory

SemesterAutumn Semester 2012
LecturersP. Nolin
Periodicityyearly recurring course
Language of instructionEnglish


AbstractBasics of probability theory and the theory of stochastic processes in discrete time
ObjectiveThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
ContentThis course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned:
Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.
Lecture notesavailable, will be sold in the course
LiteratureR. Durrett, Probability: Theory and examples, Duxbury Press 1996
J. Jacod and P. Protter, Probability essentials, Springer 2004
A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006
J. Neveu, Bases mathematiques du calcul des probabilites, Masson 1980
D. Williams, Probability with martingales, Cambridge University Press 1991