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Moderate deviations and central limit theorem for small perturbation Wishart processes
CHEN Lei,GAO Fuqing * #,WANG Shaochen
School of Mathematics and Statistics, Wuhan University, WuHan 430072
*Correspondence author
#Submitted by
Subject:
Funding: Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP) of China（No.200804860048）, National Natural Science Foundation of China (NSFC)（No.11171262）
Opened online:21 March 2012
Accepted by: none
Citation: CHEN Lei,GAO Fuqing,WANG Shaochen.Moderate deviations and central limit theorem for small perturbation Wishart processes[OL]. [21 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4470943
 
 
Let Xε be a small perturbation Wishart process,i.e., the process Xε/ ε is a Wishart process withdimension ρ/ε, starting at x/ ε. In this paper, we prove that (Xε t-X 0 t)/√￣εh2( ε) satisfies a large deviation principle, and (Xεt-X 0 t)/√￣ε converges to a Gaussian process, where h( ε)→+∞ and √￣εh( ε)→0 asε→0 We also obtain a moderate deviation principle and a functional central limit theorem for the eigenvalue process of Xε by delta method and matrix perturbation theory.
Keywords:Large deviation; moderate deviation; central limit theorem; Wishart process; eigenvalue
 
 
 

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