On the Wald's Sequential Probability Ratio Test for Levy Processes

摘要

The Wald's sequential probability ratio test (SPRT) of two simple hypotheses regarding the Levy-Khintchine triplet of a wide family of Levy processes is analyzed: we concentrate on continuous paths and pure increasing jump Levy processes. Appealing to the theory of Markov processes, we employ a general method for determining the stopping boundaries and the expected length of the SPRT for a given admissible pair (α, β) of error probabilities. The well-known results of the Wiener and Poisson sequential testing can be derived accordingly. The explicit solution for the SPRT of two simple hypotheses about the parameter p e (0, 1) of a Levy negative binomial process is shown.