Nonparametric estimation for small fractional diffusion processes with random effects

摘要

We propose a nonparametric estimation of random effects from the following small fractional diffusions dX(i)(t) = beta(i)b(X-i(t))dt + epsilon dW(i,H)(t), X-i(0) - x(0)(i), 0 <= t <= T. For i - 1, ... , N, beta(i) is random variable and (W-i,W-H(t), t >= 0, i = 1, ... , N) is are standard fractional Brownian motions with a common known Hurst index H is an element of (1/2, 1): The asymptotic behavior of the proposed estimators is established when epsilon and N are, respectively, sufficiently small and large.