A radial invariance principle for non-homogeneous random walks

Electronic Communications in Probability

Nicholas Georgiou¹ 

关键词: non-homogeneous random walk;    invariance principle;    Bessel process;   

DOI  :  10.1214/18-ECP159

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

Consider non-homogeneous zero-drift random walks in $\mathbb{R} ^d$, $d \geq 2$, with the asymptotic increment covariance matrix $\sigma ^2 (\mathbf{u} )$ satisfying $\mathbf{u} ^{\top } \sigma ^2 (\mathbf{u} ) \mathbf{u} = U$ and $\operatorname{tr} \sigma ^2 (\mathbf{u} ) = V$ in all in directions $\mathbf{u} \in \mathbb{S} ^{d-1}$ for some positive constants $U

【 授权许可】

CC BY