Moderate deviations and central limittheorem for small perturbationWishart processes  

作　　者：Lei CHEN Fuqing GAO Shaochen WANG 

机构地区：[1]School of Mathematics and Statistics, Wulhan University, Wuhan 430072, China

出　　处：《Frontiers of Mathematics in China》2014年第1期1-15,共15页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements The authors would like to thank anonymous reviewers for their valuable comments and suggestions. This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 200804860048） and the National Natural Science Foundation of China （Grant No. 11171262）.

摘　　要：Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient： dXt^ε = √εXt^εtdBt＇ ＋ dBt＇√εXt^ε ＋ ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B＇ denotes the transpose of the matrix B. In this paper, we prove that { （Xt^ε-Xt^0）/√εh^2（ε）,ε 〉 0} satisfies a large deviation principle, and （Xt^ε - Xt^0）/√ε converges to a Gaussian process, where h（ε） → ＋∞ and √ε h（ε） →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method.Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient： dXt^ε = √εXt^εtdBt＇ ＋ dBt＇√εXt^ε ＋ ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B＇ denotes the transpose of the matrix B. In this paper, we prove that { （Xt^ε-Xt^0）/√εh^2（ε）,ε 〉 0} satisfies a large deviation principle, and （Xt^ε - Xt^0）/√ε converges to a Gaussian process, where h（ε） → ＋∞ and √ε h（ε） →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method.

关 键 词：Large deviation moderate deviation central limit theorem Wishart vprocess EIGENVALUE 

分 类 号：O211.5[理学—概率论与数理统计] O211.6[理学—数学]