Stochastic Activity Month
September 2012
"Stochastic Operations Management"
Lecture Day:
Gaussian and
Levy processes and
their applications in queues, finance and risk
September 27
SPEAKERS  REGISTRATION 
ORGANIZERS
Onno Boxma  TU Eindhoven 
Michel Mandjes  Universiteit van Amsterdam 
Krzysztof Dębicki  University of Wroclaw 
Offer Kella  Hebrew University of Jerusalem 
Michel Mandjes  University of Amsterdam 
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.
11.00  11.30  Welcome  
11.30  12.15  Michel Mandjes  Transient Analysis of LévyDriven Queues  
12.15  13.15  Lunch  
13.15  14.00  Krzysztof Dębicki  Locally selfsimilar Gaussian processes: extremes and Pickands constants  
14.15  15.00  Offer Kella 
Asymptotic Expected Number of Passages of a Random Walk Through an Interval 

Krzysztof Dębicki
Locally selfsimilar 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.
Michel Mandjes
Transient Analysis of LévyDriven
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 Levydriven 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 WienerHopf factors, and have
an appealing intuitive interpretation. Then 'll analyze the socalled
quasistationary workload of the Levydriven 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 onesided 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 Levydriven tandem systems.