Simple Estimators for Parametric Markovian Trend of Ergodic Processes Based on Sampled Data

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概要

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• Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」Let X be a stochastic process obeying a stochastic differential equation of the form dX_t = b(X_t,θ)d_t + dY_t, where Y is an adapted driving process possibly depending on X's past history, and θ ∈ Θ ⊂ R^p is an unknown parameter. We consider estimation of θ when X is discretely observed at possibly non-equidistant time-points (t_i^n)_i^n=0. We suppose h_n := max1≤i≤ n(t_i^n - t_i^n_{-1}) → 0 and t_n^n → ∞ as n → ∞: the data becomes more high-frequency as its size increases. Under some regularity conditions including the ergodicity of X, we obtain \sqrt{nh_n} -consistency of trajectory-fitting estimate as well as least-squares estimate, without identifying Y. Also shown is that some additional conditions, which requires Y's structure to some extent, lead to asymptotic normality. In particular, a Wiener-Poisson-driven setup is discussed as an important special case.

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著者

• Masuda Hiroki

  Kyushu Univ. Fukuoka Jpn

• Masuda Hiroki

  Graduate School Of Mathematics Kyushu University

関連論文

• JOINT ESTIMATION OF DISCRETELY OBSERVED STABLE LEVY PROCESSES WITH SYMMETRIC LEVY DENSITY
• Simple Estimators for Parametric Markovian Trend of Ergodic Processes Based on Sampled Data

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