高斯过程驱动下桥的最小二乘参数估计(英文)

Least Squares Estimator for Bridges Driven by Gaussian Process

本文研究在高斯过程驱动下桥:d X_t=-αX_t/(T-t)dt+dG_t,0≤t<T参数0<α≤1/2估计问题,其中G是高斯过程.基于当t→T时轨道路径{X_s,s∈[0,t]}的观测量,获得参数α的最小二乘估计量α?的收敛和渐进分布结果,并得到其收敛率.

In this paper, we consider the parameter estimation problem for the parameterα of a Gaussian bridge defined as d X_t =-αX_t/（T-t）dt ＋ d G_t, 0 ≤ t T, with 0 α ≤1/2, where G is a Gaussian process. We obtain the consistency and the asymptotic distributions of the least squares estimator α of α based on the observation {X_s, s ∈ [0, t]} as t → T. Moreover,we also obtain the rate of this convergence.