VO250068 + PS250069 Stochastic Processes

Lecturer: Prof. Henk Bruin

Please email H. Bruin for further information about this course.

Announcements

The next exam possibility is on September 23, 14:00-16:00, in ???.

Schedule and Lecture Rooms

Day	Time	Lecture room		from	until
Tuesday	11:30-13:00	SR07	Lecture	2.10.2018	29.01.2019
Thursday	8:30-9:15-	SR10	Exercises	4.10.2018	24.01.2019
Thursday	9:30-10.15	SR10	Lecture	4.10.2018	24.01.2019

Contents of Course

Literature

Scripts/Background reading.

Script Jiří Černý (in German)
Script Franz Hofbauer (in German)
Script Markov chains script (in English)
Script Josef Hofbauer (in English). This script was written by students in Hofbauer's class and hasn't been proof-read in full!
P. Billingsley, Probability and Measure 3rd Edition ISBN-13: 978-0471007104 ISBN-10: 0471007102
Kai Lai Chung, Elementary probability and stochastic processes, Springer Verlag New York, 1974. ISBN 0-387-90159-0
E. Çinlar, Introduction to Stochastic Processes, Dover Publications Inc. 2013 ISBN-13: 978-0486497976 ISBN-10: 0486497976
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition 3rd Edition. ISBN-13: 978-0471257097 ISBN-10: 0471257095
G. R. Grimmet and D. R. Stirzaker, Probability and Random Processes, Oxford Science Publications 1981, Clarendon Press Oxford ISBN 0-19-853185-0
C. Norris, Markov Chains, (Cambridge Series in Statistical and Probabilistic Mathematics) Cambridge Univ. Press, ISBN-13: 978-0521633963 ISBN-10: 0521633966
G. Grimmett, D. Welsh, Probability: An Introduction, Oxford Science Publ. ISBN 0 19 853264

Assessment/Leistungsbeurteilung

Written Exam for the VO, class tests + presenting exercises on the board for Proseminar (Exercises).

Weekly Progress

Day	Material
Week 1
2/10/2018	Introduction, Poisson Limit Theorem, CLT
4/10/2018	Poisson Limit Theorem, CLT
Week 2
9/10/2018	Random walks on graphs, Gambler's Ruin	Norris, Chapter 1
11/10/2018	Exercise sheet 1-4
Week 3
16/10/2018	Gambler's Ruin/Absorbing states
18/10/2018	Finite Markov chains/communication classes Stationary distributions	Norris, Chapter 1
Week 4
23/10/2018	Henna Koivusalo will replace me this week Stopping times	Grimmett & Stirzaker Sect 7.7 and 7.9
25/10/2018	Exercise sheet 6-11
Week 5
30/10/2018	Time-reversible Markov chains	Norris, Section 1.9
1/11/2018	No class because of All Souls
Week 6
6/11/2018	Random walks on Z	Script J. Hofbauer, Section 1.1-1.5
8/11/2018	Exercise sheet 11-15
Week 7
13/11/2018	Random walks, Reflection Principle Ballot Theorem	Script J. Hofbauer, Section 1.1-1.5
15/11/2018	Cancelled
Week 8
20/11/2018	Arcsine Laws, Random walks and Brownian motion Counting processes	Script J. Hofbauer, Section 1.6
22/11/2018	Exercise sheet 15-19
Week 9
27/11/2018	Characterisations Poisson Process	Script Černý, Kapitel 3
29/11/2018	more on Poisson processes	Script Černý, Kapitel 3
Week 10
4/12/2018	Lecture by Martin Huesmann Differential equation for generating function	Grimmett and Stirzaker Section 6.8
6/12/2018	Class Test (material exercises 1-14 and variations)
Week 11
11/12/2018	Class canceled
13/12/2018	Class canceled
Week 12
8/1/2019	Birth and Death processes Differential equation for generating function	Grimmett and Stirzaker 6.11
10/1/2019	Exercise sheet 18-22
Week 13
15/1/2019	Backward/Forward equations and solutions	Grimmett and Stirzaker 6.8
17/1/2019	Exercise sheet 21,22,23,24,26
Week 14
22/1/2019	Question hour 15:00-16:30 in SR9
24/1/2019	Class Test (material exercises 15-20 and variations)
Week 15
29/1/2019	Written Exam 15:00-17:00 HS5
31/1/2019

Course material (Hand-outs/Exercises)

Exercise sheet.
Derivation of the forward and backward equations.

Updated August 16 2019