Topics in probability and statistics

There are no prerequisites.

The content consists of a selection of standard topics in advanced probability and statistics. Possible topics are:

• Convergence of ramdom variables.
• Conditional expectation and conditional distributions.
• Martingales.
• Brownian motion.
• Parameter estimation, optimality.
• Hypothesis testing, optimality.
• Asymptotic theory
  The choice depends on students' research interests.

1. J. Bertoin: Lévy processes, Cambridge : Cambridge University Press, cop. 1996.
2. R. Durrett: Probability : theory and examples, 2nd ed., Belmont (Calif.) : Duxbury Press : Wadsworth : ITP International Thompson Publ., cop. 1996.
3. S. M. Ross: Stochastic processes, 2nd ed., New York : Wiley, cop. 1996.
4. M. J. Schervish: Theory of statistics, 2nd corrected print. - New York : Springer, cop. 1997.
5. J. Shao: Mathematical statistics, 2nd ed. - New York : Springer, cop. 2010.
6. S. R. S. Varadhan: Probability theory, New York : Courant Institute of Mathematical Sciences ; Providence (Rhode Island) : American Mathematical Society, cop. 2001.

The main goal of the course is to provide students with some important topics in probability and statistics.

Znanje in razumevanje predstavljenih konceptov.
Sposobnost uporabe pridobljenega znanja in spretnosti.

Lectures, consultations, problem sessions

Writen exam (homeworks), oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111. [COBISS-SI-ID 7101017]
PERMAN, Mihael, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120. [COBISS-SI-ID 17154393]