Branching Processes

As the most basic operations, addition and multiplication have been the cornerstone of   mathematics. Similarly, random walks and Levy processes as an important kind of addition processes include about half of basic stochastic processes. In my opinion, another half should be contained in branching processes, which are an important kind of multiplication processes. Branching processes are an important class of Markov processes originating from the stochastic modeling of population, which have been widely applied in the study of random network, queue theory and finance. Thus it is necessary for us to study branching processes deeply and systematically. 

Attention:

This course will be taught in English to facilitate participation of international students. 

 

Instructor

Dr. Wei XU
Office: Rudower Chaussee 25, Haus 1, Raum 234
Email: xuwei@math.hu-berlin.de
Office hours: Need appointment

 

Lecture (Weekly)

The first lecture will take place on Friday, 20.04.18

Fri. 09:00 - 11:00 in Room 4.007 (RUD25) - Wei XU

 

Tutorial (Biweekly)

The first tutorial will take place on Friday, 27.04.18

Fri. 11:00 - 13:00 in Room 4.007 (RUD25) - Wei XU

 

Content

  • GW-processes: criticality, extinction probability and (conditional-) limit theorems
  • CB-processes: extinction probabilities, limit theorems, extreme distributions and criterion for transience or recurrence
  • Reconstruction of CB-processes: excursion reconstruction, semigroups representation and stochastic equation representation
  • Lamperti's transformations by time changes
  • Applications: Ray-Knight theorem, term structure of interest rate, cluster representations for Hawkes processes and M/G/n-systems

 

References

Lecture notes will be available during the course; good references include: 

  1. Athreya, K.B. and Ney, P.E. (1972): Branching Processes. Springer, Berlin
  2. Bansaye, V. and Meleard, S. (2015): Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior. Springer
  3. Li, Z. (2011): Measure-Valued Branching Markov Processes. Springer, Heidelberg
  4. Pardoux, E. (2015): Probabilistic Models of Population Evolution: Scaling Limits, Genealogies and Interactions. Springer

 

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