Information criteria for small diffusions via the theory of Malliavin-Watanabe. (English) Zbl 1333.62032

Summary: Information criteria based on the expected Kullback-Leibler information are presented by means of the asymptotic expansions derived with the Malliavin calculus. We consider the evaluation problem of statistical models for diffusion processes with small noise. The correction terms are essentially different from the ones for ergodic diffusion models presented in [the authors, ibid. 4, No. 1, 73–98 (2001; Zbl 1092.62595)].


62B10 Statistical aspects of information-theoretic topics
62E20 Asymptotic distribution theory in statistics
62M05 Markov processes: estimation; hidden Markov models
60H07 Stochastic calculus of variations and the Malliavin calculus


Zbl 1092.62595
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