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All talks will be held in room 306, the Integrity building (精正楼). May 31st,2016(Tuesday) Speaker: Sergey Foss( Heriot-Watt University, Edinburgh and Novosibirsk State University) Title: Two examples of communication models where heavy tails arise in the‘light-tail world‘. Abstract: I plan to discuss two models that arise in communication systems: 10:00-10:20 Tea Break 10:20-11:20 Speaker: Korshunov Dmitry（Lancaster University） Title: On Subexponential Tails for the Suprema of Negatively Driven L‘evy Processes Abstract: We study tail properties of the distribution of the supremum within finite time horizon of L‘evy process with negative drift and heavy-tailed jumps. The tail asymptotics obtained are uniform in time horizon. We show what is similar to the case of a random walk and discuss differences. Also we study similar problem for the compound renewal process and specify these results for the compound Poisson process. Applications are given to the Cram‘er-Lundberg risk model. 12:00-13:00 Lunch Speaker: Sergey Foss (Heriot-Watt University, Edinburgh and Novosibirsk State University) Title: On the tail asymptotics in generalised Jackson networks with regularly varying tail distributions of service times Abstract: We consider a generalised Jackson network with general routing and regularly varying tail distributions of service times (see e.g. F.Baccelli and SF, AnnAP, 2004 for the particular case of feedforward networks). We present new results on the exact tail asymptotics for the distribution of the stationary sojourn time (see F. Baccelli, SF and M. Lelarge, 2004, QUESTA for the distribution of the so-called maximal data). For that, we first revise basic ideas and consider a number of preliminary examples. 15:00-15:20 Tea Break 15:20-16:20 Speaker: Korshunov Dmitry（Lancaster University） Title: How heavy-tailed distributions arise in various models with light-tailed input Abstract: In this talk we discuss three interesting probabilistic models where light-tailed input generates heavy-tailed output. We say that a distribution F is light-tailed if it possesses some positive exponential moment finite. The distribution F is called heavy-tailed if all positive exponential moments are infinite. The first model is related to the Lamperti problem for Markov chains with asymptotically zero drift. Let The second model is Gaussian chaos, that is, a polynomial of standard normal variables. The simplest case is given by a product of components of normal random vector with general covariance matrix. The distribution of Gaussian chaos is usually heavy-tailed and we show how does it happen and what kind of tails should we expect. The third model is related to perpetuities:
where
Speaker: Prof.Yuebao Wang (Soochow University) Title: On closedness under convolution roots related to an infinitely divisible distribution in the distribution class 10:00-10:20 Tea Break Speaker: Prof.Dongya Cheng (Soochow University) |
Mini-workshop on Heavy-Tailed Models and Their Applications
be a time homogeneous Markov chain on 
of Lamperti type, that is, with asymptotically zero drift, that is,
as i→∞. We assume that m(i) is negative ultimately in space and such that 
is stable with stationary distribution 
. The problem is to describe asymptotic behaviour of
as i→∞. I will explain why stationary distribution of a Markov chain with asymptotically zero drift is usually heavy-tailed even if X has bounded jumps, in contrast to more classical case of asymptotically negative drift where stationary distribution is usually light-tailed. I will also explain how particular regularly varying and Weibull-type distributions arise in this context.
is a Markov modulated random walk, that is, 
are independent identically distributed random variables. Assume 
drifts to minus infinity, so that the perpetuity is well defined. The distribution of the perpetuity is always heavy-tailed. We explain the tail behaviour of this perpetuity under general conditions on 
and 
.