混合分数布朗运动驱动过程线性乘子的非参数估计
Nonparametric Estimation of Linear Multiplier for Processes Driven by Mixed fractional Brownian Motion
摘要：
本文研究了满足$dX_t=θ(t)X_tdt+\epsilond\bar W_t^H, X_0=x_0, 0\leq t \leq T$型随机微分方程的线性乘子函数$θt)$的非参数估计问题，其中$\{\bar W_T^H, t \geq 0\}$是一个具有已知Hurst指标$H$的混合分数布朗运动，并研究了估计量为$ε\rightarrow 0.$的渐近性质
英文摘要：
We study the problem of nonparametric estimation of linear multiplier function $θt)$ for processes satisfying stochastic differential equations of the type $dX_t=θ(t)X_tdt+\epsilond\bar W_t^H, X_0=x_0, 0\leq t \leq T$ where $\{\bar W_T^H, t \geq 0\}$ is a mixed fractional Brownian motion with known Hurst index $H$ and study the asymptotic behaviour of the estimator as $ε\rightarrow 0.$
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