Abstract: The main objective of the talk is to look from a unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. In particular, we will try to understand what is common between classical probabilistic results, such as the law of iterated logarithm for example, and a well-known problem in adaptive estimation called price to pay for adaptation. Why do there exist two different kinds of this price? It turned out that all of these and many others problems can be reduced to finding upper functions for a collection of positives random variables.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006