ANALYSIS
SEMINAR

" Compound
Poisson Disorder Problems with Nonlinear

Detection Delay Penalty Cost Functions"

By

Savaş Dayanık

(Bilkent
University)

Abstract: Suppose that the arrival
rate and mark distribution of a compound Poisson process suddenly change at
some unknown and unobservable time. We would like to detect the disorder time
as quickly as possible using only the observations of the compound Poisson
process. The problem is formulated in a Bayesian setting, where the detection
delay penalty is a general smooth function of

the detection delay time. Under suitable conditions, the problem is shown to be
equivalent to the optimal stopping of a finite-dimensional
piecewise-deterministic strongly Markov sufficient statistic. The solution of
the optimal stopping problem is described in detail for the compound Poisson
disorder problem with polynomial detection delay penalty function of arbitrary
but fixed degree. The results are illustrated for the case of the quadratic
detection delay penalty function..

Tea and cookies will be served before the
seminar.

Date:
Tuesday, October 19, 2010

Time: 15.40

Place: Bilkent University Mathematics Seminar Room, SA-141