SUBJECT
Title
Stochastic processes with independent increments, limit theorems
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Infinitely divisible distributions, characteristic functions. Poisson process, compound Poisson-process. Poisson point-process with general characteristic measure. Integrals of point-processes. Lévy–Khinchin formula. Characteristic functions of non-negative infinitely divisible distributions with finite second moments. Characteristic functions of stable distributions.
Limit theorems of random variables in triangular arrays.
Readings
- Y. S. Chow – H. Teicher: Probability Theory: Independence, Interchangeability, Martingales. Springer, New York, 1978.
- W. Feller: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New York, 1966.