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Infinitesimal generators for two-dimensional Lévy process-driven hypothesis testing

  • Michael Roberts
  • Indranil SenGuptaEmail author
Research Article

Abstract

In this paper, we present the testing of four hypotheses on two streams of observations that are driven by Lévy 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 Lévy 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 super-solutions and sub-solutions are computed. An application of this procedure for stochastic model is also presented in relation to the financial market.

Keywords

Lévy process Infinitesimal generator Hypothesis tests Viscosity solution Oil price 

JEL Classification

C12 C13 C62 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their careful reading of the manuscript and for suggesting points to improve the quality of the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorth Dakota State UniversityFargoUSA

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