Focus Topic: Probability Theory and its Applications

The focuses of the Institute of Mathematical Stochastics lie in the analysis of complex stochastic systems which appear in numerous fields of natural and social sciences. Amongst others the following topics are of special interest: complex networks, branching processes, percolation theory, renewal theory, statistical mechanics, random matrices, random analytic functions, extreme value theory, large deviations, stochastic approximation, stochastic geometry, optimal transport, financial and actuarial mathematics.

A path simulation of Brownian motion to visualize the iterated logarithm theorem

Courses for the specializations in Probability Theory and their Applications (WA) and Stochastic Processes (SP)

Winter semester 2019/2020

  • Prof. Dr. Mukherjee: Probability Theory II (Type I, II; WA, SP)
  • Prof. Dr. Huesmann: Stochastic Analysis (Type I, II, WA, SP)
  • Prof. Dr. Alsmeyer: Applied Stochastic Models (Type I, II, WA, SP)
  • PD Dr. Stolz: High-dimensional Statistics (Type I, II, WA, SP)

Summer semester 2020

  • PD Dr. Paulsen: Advanced Financial Mathematics (Type I,  II, WA, SP)
  • Prof. Dr. Alsmeyer: Statistical Learning (Type I, II, WA, SP)
  • Prof. Dr. Huesmann: Stochastic Mass Transport (Type I, II, WA, SP)
  • Prof. Dr. Dereich: Rough Paths and their Applications to Machine Learning (Type I, II, WA, SP)

Prerequisites

A couse on Probability Theory that provides a deep knowledge on the following subjects:

Measure and integration, stochastic independence, product spaces, Markov-kernels, 0-1 laws, martingales, laws of large numbers, weak convergence, central limit theorem.

These topcs can be found in the book Probability Theory of Prof. Dr. Achim Klenke: https://www.springer.com/de/book/9781447153603

Further information

The subject areas of the research groups are the following:

On the sites of the research groups you may find more information about courses, seminars, master-theses, etc.