Course descriptionThis course is about the mathematical foundations of randomness. Most advanced topics in stochastics and statistics rely on probability theory. The basic constructions are identical to measure theory, but there are a number of distinctly probabilistic features such as independence, notions of convergence of random variables, information contained in a sigma-algebra, conditional expectation, characteristic functions and generating functions, laws of large numbers and central limit theorems, etc.
- Random numbers, vectors, and sequences
- Integration with respect to a probability measure
- Stochastic independence and product measure
- Law of large numbers and the central limit theorem
- Conditional expectation with respect to a sigma-algebra
Time2015-2016 Period III (6 weeks)
- Lectures: Tue 10-12 and Thu 14-16 in M3 (2 x 2h lectures / week)
- Exercises: Wed 14-16 in M3 (1 x 2h exercises / week)
PrerequisitesFamiliarity with continuous functions and open sets (e.g. MS-C1540 Euklidiset avaruudet).
ExamFebruary 23 at 16:30-19:30.
(Another chance to do the exam will be April 5 at 13:00-16:00)
- J. Jacod & P. Protter: Probability Essentials. Universitext, Springer, 2004.
- D. Williams: Probability with Martingales. Cambridge University Press, 1991
Yet another alternative textbook in Finnish
- T. Sottinen: Todennäköisyysteoria. (online lecture notes)