Stochastik II

Learning and qualification objectives:

  • Knowledge of the most important classes of stochastic processes in discrete time
  • Applying  techniques from martingale theory and Markov chains 
  • Consolidation of the principles of probability theory and the modeling of random dynamic processes 
  • Understanding the basic properties of stochastic processes in continuous time, especially Brownian motion 

Lecture:

  • Mo. 09:15 - 10:45 Uhr in room 0'311 (RUD26) - D. Kreher
  • Mi. 11:15 - 12:45 Uhr in room 0'311 (RUD26) - D. Kreher

Tutorial:

  • Fr. 9:15 - 10:45 Uhr in room 3.007 (RUD25) - D. Kreher

Content:

  • Conditional expectations
  • Martingales in discrete time
  • Markov chains: recurrence, transience, invariant measures
  • Construction of stochastic processes, weak convergence of stochastic processes, invariance principle, Brownian motion

Literature: 

  • Jean Jacod & Philip E. Protter: Probability Essentials (Springer, 2004)
  • Achim Klenke: Wahrscheinlichkeitstheorie / Probability Theory (Springer, 2013)
  • David Williams: Probability with Martingales (Cambridge, University Press, 1991)
  • Richard Durrett: Probability: Theory and Examples (Duxbury Press, 1996)
  • A.N. Shiryaev: Wahrscheinlichkeit / Probability-1 (Dt. Verlag der Wissenschaft, 1988 / Springer, 2016)
  • Patrick Billingsley: Convergence of Probability Measures (Wiley, 1999)

Exercise Sheets:

Exam dates:

  • 18.02.19
  • 18.03.19