Stochastics for MSc students of Electrical Engineering

Fall semester 2020
Course code: BMETE90MX55
No. of credits: 3

Classes:
  • Tuesdays 8:30-10:00
  • Wednesdays 12:15-13:45 on even weeks (Week 2 is 16 Sept.)


  • Classes will be held online. Teams code for the course: c8fkmfv. You can also contact me by e-mail: pollux@math.bme.hu

    Schedule (preliminary, updated as the semester progresses):
    WeekTuesdaysWednesdays
    1--
    2Basic probabilityBasic probability problems
    3Probability generating function-
    4Branching processesGenerating function, branching processes problems
    5Poisson processes-
    6Poisson processes problemsCentral limit theorem, large deviations
    7Central limit theorem, large deviations problems-
    8Questions & AnswersMidterm test 1
    9Discrete time Markov chains-
    10Discrete time Markov chains problemsContinuous time Markov chains
    11Continuous time Markov chains problems-
    12StatisticsStatistics
    13Statistics problems-
    14Questions & AnswersMidterm test 2


    Final mark is based on homework assignments (10%) and two midterm tests (45% each). Details will be available in time.

    Homework: Publication times and deadlines will be available in time.

    Maximal total score is 10+45+45=100. Marks based on the total score are as follows:
  • 0-39: 1
  • 40-54: 2
  • 55-69: 3
  • 70-84: 4
  • 85-100: 5

  • 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 (pdf)

  • Lecture slides will be available as the semester progresses.

    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
  • Law of large numbers: Durrett (Probability) 2.4
  • Central limit theorem: Durrett (Probability) 3.4.1, Berry-Esseen: Durrett 3.4.4
  • Large deviations: Durrett 2.6 (Probability)
  • 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)