Identification of Nonstationary Diffusion Model by the Method of Sieves

Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

“…Kutoyants (1984b) derived asymptotic properties of kernel-type estimators of the drift term in a stochastic differential equation. In a nonstationary linear diffusion model Nguyen and Pham (1982) applied Grenander's method of sieves to the problem of estimating the drift coefficient that is a function of time. They approximated the unknown function by a finite linear combination of a given system of functions and proved consistency and asymptotic normality of the estimate.…”

“…The objective of this paper is to combine the methods used in Huebner and Rozovskii (1995) and Nguyen and Pham (1982) and construct an estimate of a coefficient that is a function of time in a model described by a stochastic parabolic equation. Suppose the process u(t, x) for t ∈ [0, T ] and x ∈ G ⊂ IR d is governed by the following equation:…”

Identification of a hereditary system with distributed delay

“…We apply his idea to a canonical example where one wants to identify the distributed delay function of a linear hereditary system. Recently, Nguyen and Pham [4] applied the method of sieves to the problem of identifying a nonstationary diffusion model.…”

Nonparametric Estimation of Trends in Linear Stochastic Systems

“…There is an extensive literature on nonparametric estimation for the drift (or trend) function, g, in a diffusion process satisfying (2) with Z as a Wiener process; see Khasminski (1980, 1981), Geman and Hwang (1983), Nguyen and Pham (1982), Beder (1987), McKeague (1986)-who allowed Z to be a general square integrable martingale, and Leskow (1989)-who considered the case of a periodic model. These authors use either Parzen-Rosenblatt type kernel estimators or Grenander (1980) sieve estimators for g, but those estimators are not directly applicable to the present setting, unless C is identically zero (in which case only g is identifiable).…”