Locally most powerful sequential tests for processes of the exponential class with stationary and independent increments

Sequential tests that are locally most powerful (LMP) for certain one-sided problems in the case of processes of the exponential class with stationary and independent increments are discussed. After having proved the existence of an LMP sequential test in the above setting each LMP test is shown to be a Wald SPRT for a family of paired (conjugate) simple hypotheses.