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A model discrimination method for processes with different memory structure. (English) Zbl 0934.60072
Summary: We develop a test for determining whether the observed sample path comes from a system with hysteresis perturbed by noise, or if it arises from a system governed by an ordinary differential equation with the same noise. A large sample size test is constructed, which is appropriate in many practical situations. Two models are considered as alternatives to the hysteresis model. An asymptotic expression for the cutoff point of the test is found using a version of the central limit theorem.
MSC:
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60K40 Other physical applications of random processes
62F05 Asymptotic properties of parametric tests
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