Let X^εbe a small perturbation Wishart process with values in the set of positive definite matrices of size m,i.e.,the process X^εis the solution of stochastic differential equation with non-Lipschitz diffusion coef...Let X^εbe a small perturbation Wishart process with values in the set of positive definite matrices of size m,i.e.,the process X^εis 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)/√εconverges to a Gaussian process,where h(ε)→+∞and√εh(ε)→0 asε→0.A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^εare also obtained by the delta method.展开更多
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.200804860048)the National Natural Science Foundation of China(Grant No.11171262).
文摘Let X^εbe a small perturbation Wishart process with values in the set of positive definite matrices of size m,i.e.,the process X^εis 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)/√εconverges to a Gaussian process,where h(ε)→+∞and√εh(ε)→0 asε→0.A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^εare also obtained by the delta method.
