2-7 September 2018
Europe/Warsaw timezone

Selected properties of integrated stochastic processes

6 Sep 2018, 15:00
3h

Speaker

Karol Capala (M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland)

Description

Brownian motion (Wiener process) and Ornstein-Uhlenbeck processes are two basic stochastic processes, which are frequently, among others, used in the statistical physics. We consider the full stochastic dynamics, i.e. a situation when a particle is described by the position and velocity. It is assumed that velocity changes according to Wiener or Ornstein-Uhlenbeck processes. Consequently, a particle position is described by an integrated stochastic process. We examine such processes in the free case. Moreover, the problem of first escape from a finite interval for integrated stochastic processes is studied. We show similarities and differences between both processes. These differences arise due to introduction of damping and are especially well visible for a free particle. In the studied range, the problem of first escape seems to be less sensitive to the process describing evolution of the velocity.

Primary author

Karol Capala (M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland)

Co-author

Dr. Bartłomiej Dybiec (M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland)

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