Hypothesis tests on high dimensional datastreams, with finance application

Abstract

In this paper, we present the testing of many hypotheses on multiple streams of observations that are driven by Lévy processes. This is applicable for sequential decisionmaking on the state of multi-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to 2n possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.