Strong invariance principle for a counterbalanced random walk  

作　　者：TAN Hui-qun HU Zhi-shui DONG Liang 

机构地区：[1]International Institute of Finance,School of Management,University of Science and Technology of China,Hefei 230026,China [2]Center for Basic Teaching and Experiment,Nanjing University of Science and Technology,Jiangyin 214443,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第2期370-380,共11页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11671373).

摘　　要：We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(v(n))with probability 1−p,where v(n)is a uniform random variable on{1;…;n−1}.We apply martingale method to obtain a strong invariance principle forS_(n).

关 键 词：random walk MARTINGALE invariance principle 

分 类 号：O211.6[理学—概率论与数理统计]