On record events and extremes for dynamical systems

Speaker: Associate Professor Mark Holland
Affiliation: University of Exeter

Abstract

Record events occur in many situations, such as in temperature records within weather, financial asset price records, and in sporting events, e.g. the 100m sprint. Within probability and random processes, the study of records can be formalised and their limit distributions studied. If we take a sequence of random variables $X_1,\ldots, X_n$, a record time corresponds to the time $t$ where $X_t>max(X_1,\ldots, X_{t-1})$, i.e. $X_t$ exceeds all values occurring before time t. A topic of interest is the distribution of such record times, and corresponding record values. In the talk, we review classical results which are part of a wider extreme value theory.  We consider processes that are independent, and identically distributed. Then we mention research progress when the process $(X_n)$ is generated by a deterministic dynamical system.