In a reduction method is proposed that takes intoaccount the underlying statistical structure.An approach of improving the sequential hypothesis testing in the Bayesian case ispresented in. But it is often difficult to handle all the data as represented by a σ -algebra as theactual amount may be very large. For a sequentialdecision problem, it is assumed that the amount of available information is increasing withtime. Thesequential probability ratio test is revisited and improved in various works. For the second approach, no such assumption is made and theoptimal solution is known to be given by the sequential probability ratio test (see ). For the first approach, each hypothesis is assignedwith an a priori probability. There are a couple of primary approaches to this problem, ∗ Email: † Email: a r X i v. An objective for the analysis of such test is to minimize the number ofobservations required to make a decision subject to a given tolerance level described asType I and Type II errors. Consequently, the test is carriedout sequentially. As described in, a sequential test of a hypothesis meansany statistical test that gives a specific rule, at any stage of the experiment for makingone of the three decisions: (1) to accept the null hypothesis H, (2) to reject H, (3) tocontinue the experiment by making additional observation. One of the most classical problems arising in statistical sequential analysis is the sequentialhypothesis testing (see ). L´evy process, infinitesimal generator, hypothesis tests, viscosity solution,oil price. An applica-tion of this procedure for stochastic model is also presented in relation to the financialmarket. Bounds for infinitesimalgenerators in terms of super-solutions and sub-solutions are computed. Infinitesimal generators are presented and analyzed. In either case, these give rise to four pos-sibilities. In another, each sensor receives data drivenby L´evy processes with large or small jumps. In one case, each sensor receives or doesnot receive a signal obstructed by noise. This is applicable for sequential decisionmaking on the state of two-sensor systems. In this paper, we present the testing of four hypotheses on two streams of obser-vations that are driven by L´evy processes. Michael Roberts ∗, Indranil SenGupta † Department of MathematicsNorth Dakota State UniversityFargo, North Dakota, USA.November 20, 2019 IInfinitesimal generators for two-dimensionalL´evy process-driven hypothesis testing
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