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Estimation of parameters for discretely observed diffusion processes with a variety of rates for information

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Abstract

A specific form of stochastic differential equation with unknown parameters are considered. We do not necessarily assume ergodicity or recurrency, and any moment conditions for the true process, but some tightness conditions for an information-like quantity. The interest is to estimate the parameters from discrete observations the step size of which tends to zero. Consistency and the rate of convergence of proposed estimators are presented. The rate is deduced naturally from the rate for the information-like quantities.

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Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Yasutaka Shimizu

  2. Japan Science and Technology Agency, CREST, Sanbancho, Chiyoda-ku, Tokyo, 102-0075, Japan

    Yasutaka Shimizu

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  1. Yasutaka Shimizu
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Correspondence to Yasutaka Shimizu.

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Shimizu, Y. Estimation of parameters for discretely observed diffusion processes with a variety of rates for information. Ann Inst Stat Math 64, 545–575 (2012). https://doi.org/10.1007/s10463-010-0323-4

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  • DOI: https://doi.org/10.1007/s10463-010-0323-4

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