Optimal sequential change-detection for fractional diffusion-type processes
Statistics Theory
2012-07-13 v2 Methodology
Statistics Theory
Abstract
We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary processes with continuous paths and apply this general result to the special case of fractional diffusion-type processes. As a by-product, we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H + 1/2 after the change.
Cite
@article{arxiv.1102.0598,
title = {Optimal sequential change-detection for fractional diffusion-type processes},
author = {Alexandra Chronopoulou and Georgios Fellouris},
journal= {arXiv preprint arXiv:1102.0598},
year = {2012}
}
Comments
23 pages