Testing hypothesis for the shift parameter in diffusion processes. (English) Zbl 0632.62085

The problem of testing hypotheses for diffusion type processes when the unknown parameter plays the role of shift is considered. The parametric family of distributions is LAMN in this model and there are no satisfactory results for asymptotic optimality of the tests in the literature. Using the conditional inference approach a test is constructed which is asymptotically optimal under the conditional distribution. Numerical results are presented to illustrate the problem.


62M02 Markov processes: hypothesis testing
62F05 Asymptotic properties of parametric tests
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