Sequential tests that are LMP for certain one-sided testing problems are discussed. In all cases considered, the stopping rule is the first time a certain random walk leaves a bounded interval. (Thus various inequalities and approximations due to Wald can be utilized in obtaining properties of these tests.) For models in a one-parameter exponential family, each LMP sequential test is shown to be a Wald SPRT for a family of paired (conjugate) simple hypotheses.
"Locally Most Powerful Sequential Tests." Ann. Statist. 3 (2) 373 - 381, March, 1975. https://doi.org/10.1214/aos/1176343063