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