Mini-course: Regularly varying functions with applications in probability theory
Professor O.I. Klesov from National Technical University of Ukraine "Igor Sikorsky Kyiv Politechnic Institute" will give a mini-course on the following topic:
We discuss the notion of regularly varying functions and some applications in probability theory. Some of the topics to be discussed are in order. Note however that not all topics will be discussed in full detail. The final choice of topics will depend on the time available.
Time and place: – ,
Niels Henrik Abels hus: Undervisningsrom 1119
PART 1: \(\mathit{RV}\) FUNCTIONS IN LIMIT THEOREMS
Central limit theorem
stable limit laws
Relative stability (Saint-Petersburg paradox)
Extremes
Records
PART 2: \(\mathit{RV}\) FUNCTIONS AND CAUCHY FUNCTIONAL EQUATION
Additive functions
Differentiable additive functions
Continuous additive functions
Monotone additive functions
Non-measurable additive functions
PART 3: FURTHER APPLICATIONS OF \(\mathit{RV}\) FUNCTIONS
Interest rate
Memory less distributions
Distribution of attaining zero for stochastic processes
Buffon neddle problem
Formal justice
PART 4: BASIC RESULTS FOR \(\mathit{RV}\) FUNCTIONS