Institute for Applied Mathematics  / Probability Theory and Stochastic Analysis  /  Patrik Ferrari
University of Bonn Institute for Applied Mathematics
 
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Hauptseminar Angewandte Stochastik - Ferrari, SS 2009

Zeit und Ort Donnerstag, 12-14, Seminarraum 011 LWK
BeginnErste Semesterwoche: 16. April 2009
BetreuungPatrik Ferrari (LWK 347) und Nicola Kistler (LWK 342)
Pre-Seminar MeetingMontag, 12-12:30 (nur für die Studenten, die am kommenden Donnerstag ein Seminar halten)

Inhalt

Continuous time Markov Chains

1. Continuous time random processes, properties of exponential distribution 23. April 2009 Bogdanov
2. Poisson process on R and birth processes 23. April 2009 Wiens
3. Jump chain, holding times and explosion 30. April 2009 Anschlag
4. Forward and backward equations 30. April 2009 Fuchs
5. Hitting times, absorption probabilities, recurrence and transience 7. Mai 2009 Jansen
6. Invariant distributions, convergence to equilibrium and ergodic theorem 7. Mai 2009 Stümper
7. Application to Monte Carlo, H-theorem for Metropolis algorithm 14. Mai 2009 Veken
8. Application to queues 14. Mai 2009 Becker

Point processes

9. Definition of point processes and examples like Poisson point process 28. Mai 2009 Winter
10. Correlation function, relation with moments, gap probability; determinantal class 28. Mai 2009 Vogelsang
11. Application to GUE random matrix eigenvalues 18. Juni 2009 Nohn
12. Non-coinciding probabilities for birth-death processes: Karlin-McGregor theorem (and its graph generalization) 18. Juni 2009 Beisegel
13. Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, Teil I 25. Juni 2009 Lechtenberg
14. Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, Teil II 25. Juni 2009 Fei

Renewals

15. Definition of Renewals, renewal equation and theorem 2. Juli 2009 Günther
16. Applications of renewal processes 2. Juli 2009 Heidebrecht
17. Renewal-reward processes 9. Juli 2009 Beins
18. Renewals and queues: some applications 9. Juli 2009 Eckstein

Literatur

• Zu 1-8: J.R. Norris, Markov Chains, Cambridge Press
• Zu 9,15-19: G. Grimmett and D. Stirzaker, Probability and Random Processes, Oxford Press
• Zu 9-11: P.L. Ferrari, TU Lecture on random matrices 2007, and Lecture notes of the Beg Rohu Summer School 2008
• Zu 12: S. Karlin and L. McGregor Coincidence probabilities, Pacific J. 9 (1959) 1141-1164.
• Zu 13-14: D. Aldous and P. Diaconis Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem, Bull. Amer. Math. Soc. 36 (1999) 413-432.