Speaker:
Stefan Hollands
Coordinator:
Jörg Lehnert
Address:
Inselstraße 22
04103 Leipzig
Germany
Contact:
+49(0)341-9959-641
+49(0)341-9959-658
IMPRS
Lectures in the Summer Semester 2014
IMPRS Ringvorlesung "Probability theory"
The aim of this course is to give an overview of some basic concepts and results in probability. Prerequisites for this lectures: Measure theory.
Time and location:
- Lectures: Monday 13:30 - 15:00 in room G 10 (MPI MiS)
- Tutorial (Florent Barret): Thursday 9:15 - 10:45 in room A 02 (MPI MiS)
- Please note: there are no lectures on the 21.04.2014, 26.05.2014 and the 09.06.2014
Videos from all lectures
Every lecture will be recorded and can be viewed later.
For more info, streaming and download see the media WWW page at the MPI MIS.
Artem Sapozhnikov
- Probability space, random variable, expectation, independence, Borel-Cantelli lemma
- Types of convergence of random variables, weak and strong laws of large numbers, Cramer's large deviations theorem
- Characteristic functions, central limit theorem
- Infinitely divisible and stable distributions
- Dates: 07.04.2014, 14.04.2014, 28.04.2014, 05.05.2014
Felix Otto
- Conditional expectation and probability
- Martingales
- Markov chains, random walk
- Dates: 12.05.2014, 19.05.2014, 02.06.2014, 16.06.2014
Max von Renesse
- Continuous time Markov processes: Markov Kernels, Kolmogorov Consistency, Generators
- Brownian Motion: Levy Construction, Strong Markov Property, Reflection Principle
- Path regularity of Brownian Motion: Kolmogorov-Chentsov and Non-Differentiability (Paley-Wiener-Zygmund), Law of the Iterated Logarithm
- Connection between Brownian Motion and PDE: Heat and Poisson Equation in regular Domains. Recurrence-Transience of BM.
- Dates: 23.06.2014, 30.06.2014, 07.07.2014, 14.07.2014