Probability theory

Unit Coordinator: Matthias Schulte
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 2
Year: 1
Campus: Hamburg University of Technology
Language: English
Aims:

This course provides an introduction to probability theory and stochastic processes with special emphasis on applications and examples.

The first part covers some important concepts from measure theory, stochastic convergence and conditional expectation, while the second part deals with some important classes of stochastic processes. 

Content:
  • Measure and probability spaces
  • Integration and expectation
  • Types of stochastic convergence
  • Law of large numbers
  • Central limit theorem
  • Radon-Nikodym theorem
  • Conditional expectation
  • Martingales
  • Markov chains
  • Poisson processes 
Pre-requisites:

Familiarity with the basic concepts of probability

 

Reading list:
  • H. Bauer, Probability theory and elements of measure theory, second edition, Academic Press, 1981.
  • A. Klenke, Probability Theory: A Comprehensive Course, second edition, Springer, 2014.
  • G. F. Lawler, Introduction to Stochastic Processes, second edition, Chapman & Hall/CRC, 2006.
  • A. N. Shiryaev, Probability, second edition, Springer, 1996. 

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