401-3601-00L Probability Theory
Semester | Autumn Semester 2012 |
Lecturers | P. Nolin |
Periodicity | yearly recurring course |
Language of instruction | English |
Abstract | Basics of probability theory and the theory of stochastic processes in discrete time |
Objective | This 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. |
Content | This 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 notes | available, will be sold in the course |
Literature | R. 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 |