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Strong invariance principle for a counterbalanced random walk

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We study a counterbalanced random walk Šn=(X)1+···+(X)n,which is a discrete time non-Markovian process and (X)n are given recursively as follows.For n≥2,(X)n is a new independent sample from some fixed law μ≠0 with a fixed probability p,and (X)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 for Šn.

random walkmartingaleinvariance principle

TAN Hui-qun、HU Zhi-shui、DONG Liang

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International Institute of Finance,School of Management,University of Science and Technology of China,Hefei 230026,China

Center for Basic Teaching and Experiment,Nanjing University of Science and Technology,Jiangyin 214443,China

国家自然科学基金

11671373

2024

高校应用数学学报B辑(英文版)
浙江大学 中国工业与应用数学学会

高校应用数学学报B辑(英文版)

影响因子:0.146
ISSN:1005-1031
年,卷(期):2024.39(2)
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