Least squares estimation for $\alpha$-weighted fractional Brownian bridge
HAN Jing-qi1, SHEN Guang-jun2, YAN Li-tan3
1. Dept. of Info. Sci.&Tech., Donghua Univ., Shanghai 201620, China
2. Dept. of Maths, Anhui Normal Univ., Wuhu 241000, China
3. Dept. of Math., Donghua Univ., Shanghai 201620, China
Abstract In this paper, the asymptotic properties of $\widehat{\alpha}$ are considered, which is a least squares estimator for the parameter $\alpha$ of a weighted fractional bridge $$X_0=0,~~ \text{d}X_t=-\alpha\frac{X_t}{T-t}\text{d}t +\text{d}B^{a,b}_t, \ \ 0\leq t0, T>0$. The estimator has various convergence depending on the value of $\alpha$ as $t\rightarrow T.$ The rate of corresponding convergence is proved as well.
HAN Jing-qi, SHEN Guang-jun, YAN Li-tan. Least squares estimation for $\alpha$-weighted fractional Brownian bridge. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 432-444.
