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In this paper, we present the testing of four hypotheses on two streams ofobservations that are driven by L\'evy processes. This is applicable forsequential decision making on the state of two-sensor systems. In one case,each sensor receives or does not receive a signal obstructed by noise. Inanother, each sensor receives data-driven by L\'evy processes with large orsmall jumps. In either case, these give rise to four possibilities.Infinitesimal generators are presented and analyzed. Bounds for infinitesimalgenerators in terms of \emph{super-solutions} and \emph{sub-solutions} arecomputed. An application of this procedure for the stochastic model is alsopresented in relation to the financial market.

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