Stochastic Processes

Summer Semester 2026

Summary

This class gives an introduction to theory and application of stochastic processes, including martingales, Brownian motion, Poisson processes, and point processes.

Textbooks

  • J. Humpherys, T.J. Jarvis, Foundations of Applied Mathematics, Vol. 2, Algorithms, Approximation, Optimization, Society for Industrial and Applied Mathematics, 2020 (Chapter 5 for first part of course)
  • Z. Brzeźniak, T. Zastawniak, Basic Stochastic Processes, Springer, 1999
  • R.P. Dobrow, Introduction to Stochastic Processes with R, Wiley, 2016

Grading

  • The grade for this class is determined by a final written exam.
  • Successful submission of weekly exercises will add a grade bonus of 1/3 of a grade step to your final grade.
  • There will be a mock exam 3-4 weeks before the final exam. A passing grade on the mock exam will add another grade bonus of 1/3 of a grade step to your final grade.
  • Note that the pass/fail decision is not affected by the bonus, and the top grade can be achieved without the bonus.

Topics (tentative, subject to change!)

Mon, April 13, 2026

Review of discrete probability, see notes

Thu, April 16, 2026

Introduction to proability theory: axioms of discrete probability, conditional probability (HJE 5.1, 5.2.1, 5.2.2)

Mon, April 20, 2026

Law of total probability, Bayes’ rule, independence, discrete random variables, expectation (HJE 5.2.3, 5.2.4, 5.3, 5.4 in parts)

Tue, April 21, 2026

In class discussion, Exercise 1

Thu, April 23, 2026

Expectation, variance, Bernoulli trials, binomial distribution (HJ 5.4, 5.5.1, 5.5.2)

Mon, April 27, 2026

no class

Thu, April 30, 2026

no class

Mon, May 04, 2026

no class

Thu, May 7, 2026

TBA

Mon, May 11, 2026

TBA

Tue, May 12, 2026

TBA

Thu, May 14, 2026

public holiday

Mon, May 18, 2026

TBA

Thu, May 21, 2026

TBA

Mon, May 25, 2026

public holiday

Thu, May 28, 2026

TBA

Mon, June 1, 2026 TBA

TBA

Tue, June 2, 2026

TBA

Thu, June 4, 2026

public holiday

Mon, June 8, 2026

TBA

Thu, June 11, 2026

TBA

Mon, June 15, 2026

TBA

Thu, June 18, 2026

TBA

Mon, June 22, 2026

TBA

Thu, June 25, 2026

TBA

Mon, June 29, 2026

TBA

Thu, July 2, 2026

TBA

Mon, July 6, 2026

TBA

Thu, July 9, 2026

TBA

Mon, July 13, 2026

TBA

Thu, July 16, 2026

TBA