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Journal Articles Stochastics and Stochastics Reports Year : 2000

Small noise asymptotics of the GLR test for off-line change detection in misspecified diffusion processes

Abstract

We consider the problem of the non-sequential detection of a change in the drift coefficient of a stochastic differential equation, when a misspecified model is used. We formulate the generalized likelihood ratio (GLR) test for this problem, and we study the behaviour of the associated error probabilities (false alarm and nodetection) in the small noise asymptotics. We obtain the following robustness result: even though a wrong model is used, the error probabilities go to zero with exponential rate, and the maximum likelihood estimator (MLE) of the change time is consistent, provided the change to be detected is larger (in some sense) than the misspecification error. We give also computable bounds for selecting the threshold of the test so as to achieve these exponential rates.
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Dates and versions

hal-00652116 , version 1 (14-12-2011)

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Fabien Campillo, Yuri Kutoyants, François Le Gland. Small noise asymptotics of the GLR test for off-line change detection in misspecified diffusion processes. Stochastics and Stochastics Reports, 2000, 70 (1--2), pp.109--129. ⟨10.1080/17442500008834247⟩. ⟨hal-00652116⟩
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