Overview on results and open problems related to heavy-tailed distributions

Sergey Foss (Heriot-Watt University Edinburgh)
Wednesday, May 14, 2014 - 6:00pm
TU Berlin, Room MA041, Straße des 17. Juni 136, 10623 Berlin

I will speak about various topics related to heavy tails, formulate some results and hypotheses, and introduce a number of open problems. I will start with asymptotic analysis of tail probabilities for the supremum M = supn Sn of a random walk S0 = 0, Sn = X1 + ... + Xn given M is finite a.s., and review the five main cases, two cases for heavy-tailed distributions and three cases for light-tailed distributions. Then I formulate open questions related to the ”intermediate” light-tailed case.Second, I will consider sums and maxima of dependent random variables in the presence of heavy tails, discuss general assumptions related to ”conditional independence” and provide examples. Third, I will talk about the distributional asymptotics for time and value of an overshoot over a high level, for a modulated random walk with heavy-tailed distributions. 

If time allows, I’ll also talk about a number of open problems on the tail asymptotics for a number of characteristics of multi-dimensional stochastic queues and networks.