Prof. Dr. Alexander Bulinski
Time and Place
Tuesday, 10-12 am in He220
Wednesday, 8-10 am in HeE60
4 hours lecture and 2 hours excercise
Credit points: 4
Stochastics I, Stochastics II
Master students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"
- Varous definitions of Markov processes (with discrete and continuous time).
- Important examples of Markov processes (processes with independent increments, Brownian motion, Poisson process etc.).
- Homogeneous Markov chains. Semigroup of transition matrices. Generator.
- Some models involving Markov chains.
- Competition theorem for Poisson processes. The Doob construction of Markov chain.
- Limit theorems for Markov chains.
- Markov processes and martingales.
- The optimization problems. Simulated annealing.
- Hidden Markov models, their applications.
- Introduction to Markov random fields.
- B.A.Berg. Markov Chain, Monte Carlo Simulations and Their Statistical Analysis. World Scientific. 2004.
- P.Brémaud. Markov chains. Gibbs Fields, Monte Carlo Simulation, and Queues. Springer. 2005.
- A.Bulinski, A.Shiryaev. Theory of Stochastic Processes. FIZMATLIT. 2005 (in Russian).
- E.Pardoux. Markov Processes and Applications. Algorithms, Networks, Genome and Finance. J.Wiley. 2008.
- D.W.Stroock. An Introduction to Markov Processes. Springer. 2005.
- Alexander Bulinski
- Office hours: on appointment
- Phone: tba
- The lecture on Tuesday, 14th of January, 2014, takes place in room N24/131.