摘要：Let X be a stochastic process obeying a stochastic differential equation of the form dX t = b ( X t , θ) dt + 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 ( tni ) n i =0. We suppose hn := max1 ≤ i ≤ n ( tni − tn i − 1) → 0 and tnn → ∞ as n → ∞: the data becomes more high-frequency as its size increases. Under some regularity conditions including the ergodicity of X , we obtain √ nhn -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.
