Orateur
Prof.
Nicole El Karoui
(UPMC)
Description
We consider the non-Bayesian quickest detection problem of an unobservable time
of change in the rate of an inhomogeneous Poisson process. We seek a stopping
rule that minimizes the robust Lorden criterion. The latter is formulated in terms
of the number of events until detection, both for the worst-case delay and the false
alarm constraint. In the Wiener case, such a problem was solved using the so-
called cumulative sums (cusum) strategy by many authors (Moustakides (2004),
or Shyraiev (1963,..2009)). In our setting, we derive the exact optimality of the
cusum stopping rule by using finite variation calculus and elementary martingale
properties to characterize the performance functions of the cusum stopping rule in
terms of scale function. These are solutions of some delayed differential equations
that we solve elementary. The case of detecting a decrease in the intensity is easy to
study because the performance functions are continuous. In case of increase where
the performance functions are not continuous, martingale properties require using a
discontinuous local time. Nevertheless, from an identity relating the scale functions,
the optimality of the cusum rule still holds. Numerical applications are provided.
This is joint work with S.Loisel (ISFA) and Y.Sahli (ISFA).
Auteur principal
Prof.
Nicole El Karoui
(UPMC)
