PROBABILITY
The goal of this course is to introduce the students to essential concepts, terms and
results of probability theory.
It covers the material for the qualification exam in theory of probability as a part of
doctoral program in mathematics.
After successfully passed exam students will be able to:

demonstrate knowledge and understanding of the concepts, techniques and
essential results related to theory of probability and random process

use mathematical literature related to probability subjects independently, in
Croatian and English language.
Contents of the course:
Laws of large numbers. Central limit theorems. Introduction to random processe.
Stopping times. Random walks. Introduction to martingales. Essentials of Markov
chains. Brownian motion.
References:
R. Durrett, Probability Theory and Examples, Wadsworth & Brooks/Cole, 1991 (2nd
ed 1996).
B.Fristedt, L. Gray., A Modern Approach to Probability, Birkhauser, Basel, 1997.
O. Kallenberg, Foundation of Probability Theory, Springer-Verlag, 1997.
N.Sarapa, Teorija vjerojatnosti, Školska knjiga, Zagreb, 1984.