Infinitesimal generators for two-dimensional L\'evy process-driven hypothesis testing

TL;DR

This paper develops methods using infinitesimal generators to test four hypotheses in two-dimensional systems driven by Lévy processes, applicable to sensor decision-making and financial models.

Contribution

It introduces a novel approach to hypothesis testing with Lévy process-driven data using bounds on infinitesimal generators, extending existing methods.

Findings

Bounds for infinitesimal generators are derived using super- and sub-solutions.

The approach is applied to a financial market stochastic model.

The methodology enhances decision-making in sensor and financial systems.

Abstract

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by L\'evy processes. This is applicable for sequential decision making on the state of two-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 L\'evy processes with large or small jumps. In either case, these give rise to four possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of \emph{super-solutions} and \emph{sub-solutions} are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.