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)