Stochastic Activity Month

September 2012

"Stochastic Operations Management"

Lecture Day:

Gaussian and Levy processes and
their applications in queues, finance and risk

September 27

ORGANIZERS

SPEAKERS

REGISTRATION

Please fill in the online registration form by following the link to the TU/e website. There is no registration fee for this lecture day.

(Preliminary) PROGRAMME

ABSTRACTS

Krzysztof Dębicki

Locally self-similar Gaussian processes: extremes and Pickands constants

Offer Kella

Asymptotic Expected Number of Passages of a Random Walk Through an Interval

We develop a new result concerning the asymptotic expected number of passages of a finite or infinite interval (x, x + h] as x goes to infinity for a random walk with increments having a positive (and finite) expected value. If the increments are distributed like X, then the limit for a finite h>0 turns out to have the attractive form E(min(|X|,h))/EX, which unexpectedly is independent of h for the special case where |X|<b almost surely and h > b. When h is infinite, the limit is E(max(X, 0))/EX. For the case of a simple random walk, a more pedestrian derivation of the limit can be given. Joint work with Wolfgang Stadje.

PRESENTATION

Michel Mandjes

Transient Analysis of Lévy-Driven Queues

This talk includes joint work with Krzysztof Debicki, Peter Glynn, Offer Kella, Zbigniew Palmowski and Tomasz Rolski. In this talk I'll treat several topics related to the transient analysis of Levy-driven queues. I start by pointing out how, in terms of transforms, the transient distribution can be uniquely characterized for the (general) situation that jumps to both sides are allowed -- the resulting expressions are in terms of the Wiener-Hopf factors, and have an appealing intuitive interpretation. Then 'll analyze the so-called quasi-stationary workload of the Levy-driven queue: assuming the system is in stationarity, we study its behavior conditional on the event that the busy period in which time 0 is contained has not ended before time t, as t -> inf. For the spectrally one-sided cases explicit results are obtained; for instance in the case of Brownian input, we conclude that the corresponding workload distributions at time 0 and t are both Erlang(2). Then I'll present results on the workload correlation function, in terms of structural properties, as well as an efficient importance sampling algorithm. Time permitting, I'll conclude with an analysis of the transient workload in Levy-driven tandem systems.