Stochastics for MSc students of Electrical Engineering
Fall semester 2021
Course code: BMETE90MX55
No. of credits: 3
Classes:
Tuesdays 8:30-10:00, room E402
Wednesdays 12:15-13:45 on even weeks (Week 2 is 15 Sept.), room E304-305
You can contact me by e-mail: pollux@math.bme.hu
Office hours: Tuesdays 14:00-15:00, room IB115 (building I).
Requirements and general information
Lecture slides (available as the semester progresses):
01 - Basic Probability 1.pdf
02 - Basic Probability 2.pdf, lecture recording
03 - Generating Functions.pdf
04 - Branching Processes.pdf
05 - Poisson Processes.pdf
06 - Concentration Theorems.pdf
07 - Markov Chains.pdf
08 - Continuous Time Markov Chains.pdf
09 - Statistics I.pdf
10 - Statistics II.pdf
11 - Statistics III.pdf
Materials that can (and should) be used during the semester and the midterm tests:
Special distributions (pdf)
Statistical tests (pdf)
Statistical tables (z, t, chi-square) (pdf)
Problem sheets:
1. Basic probability problems 1 (pdf), some results (pdf)
2. Basic probability problems 2 (pdf), some results (pdf)
3. Generating function problems (pdf), some results (pdf)
4. Branching process problems (pdf), some results (pdf), even more results (pdf)
5. Poisson process problems (pdf), some results (pdf)
6. Concentration theorems problems (pdf), some results (pdf)
Sample problems for Midterm test 1 (pdf), solutions (pdf)
7. Markov chains problems (pdf), some results (pdf)
8. Continuous time Markov chains problems (pdf), extra problems, some results (pdf)
9. Statistics I problems (pdf)
10. Statistics II problems (pdf)
11. Statistics III problems (pdf)
For specific topics, I recommend further reading (see the list of books below). I recommend Kulkarni wherever applicable. In general, the other books are more detailed and more theoretical than expected; focus on definitions, main theorems and examples rather than on proofs and lemmas.
Basic probability: Durrett (Probability) chapters 1.1, 1.2, 1.3, 1.6, 2.1 (pages 37-38)
Probability generating function: Grinstead-Snell 10.1 (from subsection Ordinary Generating Function)
Branching processes: Grinstead-Snell 10.1
Poisson process: Durrett (Stochastic Processes) 2.2, Kulkarni 3
Concentration theorems: Durrett (Probability) 2.4, 3.4.1, 3.4.4, 2.6
Discrete time Markov chains: Durrett (Probability) 6.1-6.7, Ross 4.1-4.6, Kulkarni 2.1-2.6
Continuous time Markov chains: Ross 6.1-6.5, Kulkarni 4.1-4.7, 6.3
Recommended reading:
R. Durrett: Probability: Theory and Examples. 4th edition (Cambridge University Press, 2010)
R. Durrett: Essentials of Stochastic Processes. 3rd edition (Springer, 2016)
W. Feller: An Introduction to Probability Theory. Vol 1, 3rd edition (Wiley, 1968)
W. Feller: An Introduction to Probability Theory. Vol 2, 3rd edition (Wiley, 1971)
C. M. Grinstead and J. L. Snell: Introduction to Probability, 2nd ed. (AMS, 1997)
V. G. Kulkarni: Introduction to Modeling and Analysis of Stochastic Systems, 2nd edition (Springer, 2011)
Sheldon Ross: Introduction to Probability Models (Academic Press, Elsevier 2006)
Bhattacharyya, Johnson: Statistical principles and Methods (Wiley, 1987)
A. W. van der Vaart: Asymptotic Statistics (Cambridge Uniersity Press, 1998)