Theoretical and Mathematical Physics

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WP33 Stochastic Processes (ME2)

The module covers the following topics: Weak convergence, compactness criteria, Markov processes: recurrence and transience, harmonic functions, stationary processes, ergodic theorem for Markov chains, stochastic processes in continuous time: renewal processes, Poisson process, Levy processes, Brownian motion, Donsker's invariance principle, Martingales and stopping times in continuous time, stochastic integral with Brownian motion as integrator, Ito formula. Students learn to construct mathematical models and to analyze complex random phenomena, especially with time dependencies.
  • WS
  • 9ECTS