Lecturer

Prof. Dr. Alexander Bulinski

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Time and Place

Lecture (January 13th to February 7th, 2014)
Monday, 2-4 pm in O28/2002

Tuesday, 10-12 am in He220

Excercise session
Wednesday, 8-10 am in HeE60

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Type

 4 hours lecture and 2 hours excercise

Credit points: 4

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Prerequisites

Stochastics I, Stochastics II

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Intended Audience

Master students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"

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Contents

• 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.

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Requirements

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Exam

tba

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Problem Sheets

tba

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Literature

• 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.