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IMPRS Ringvorlesung: Summer semester 2014

  • Artem Sapozhnikov
  • Felix Otto
  • Max von Renesse
G3 10 (Lecture hall)

Abstract

About this lecture
Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field.

Topics

The aim of this course is to give an overview of some basic concepts and results in probability.

  • 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
  • Felix Otto
    • Conditional expectation and probability
    • Martingales
    • Markov chains, random walk
  • 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.

Date and time info
Monday 13:30 - 15:00

Prerequisites
Measure theory

Links

lecture
01.04.14 31.07.14

Regular lectures Summer semester 2014

MPI for Mathematics in the Sciences / University of Leipzig see the lecture detail pages

See Details

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail