28.09.2018

Probability and Stochastics

Probability theory (or stochastics) is the mathematical theory of randomness. It is a major research subject in pure mathematics where probability interacts with other fields, like partial differential equations, and real and complex analysis. But it is also an important part of applied mathematics as stochastics analyses and models systems and processes. Therefore stochastics is used in many disciplines such as statistics, physics, economics and computer science.

In our days there is an increasing demand in the society for mathematicians with a strong knowledge in probability theory, a good understanding of applications of stochastics and a receptive attitude to new theories and problems. At our university, the research in stochastics focuses on stochastic analysis and its interactions with analysis and to applications in complexity theory, numerics and statistics.

Members

Former members:
  • Rainer Avikainen, Mika Hujo, Mikko Kuronen, Lasse Leskelä, Teemu Pennanen, Eero Saksman, Heikki Seppälä, Juha Ylinen

Research

The main research topics of the Stochastics group are

Stochastic Analysis and SDEs

  • Stochastic Analysis on the Itô-Wiener space (Brownian motion and Lévy Processes)
  • Backward Stochastic Differential Equations
  • Besov Spaces and Interpolation Theory
  • Harmonic Analysis and Probability in Banach Spaces
  • Approximation of Stochastic Processes

Computational statistics and simulation methods

  • Probability and Statistical Applications
  • Monte Carlo methods
  • Markov Chains
  • Stochastic Approximation

Publications

Publications of the group can be found on the arXiv preprint server and the TUTKA database. The most up-to-date information is available on the members' personal web pages. Some of the recent publications.