26 research outputs found
Tail behaviour of the area under a random process, with applications to queueing systems, insurance and percolations
The areas under workload process and under queuing process in a single server
queue over the busy period have many applications not only in queuing theory
but also in risk theory or percolation theory. We focus here on the tail
behaviour of distribution of these two integrals. We present various open
problems and conjectures, which are supported by partial results for some
special cases
Kink estimation in stochastic regression with dependent errors and predictors
In this article we study the estimation of the location of jump points in the
first derivative (referred to as kinks) of a regression function \mu in two
random design models with different long-range dependent (LRD) structures. The
method is based on the zero-crossing technique and makes use of high-order
kernels. The rate of convergence of the estimator is contingent on the level of
dependence and the smoothness of the regression function \mu. In one of the
models, the convergence rate is the same as the minimax rate for kink
estimation in the fixed design scenario with i.i.d. errors which suggests that
the method is optimal in the minimax sense.Comment: 35 page