Moderate deviations and central limit theorem for small perturbation Wishart processes

Let X (epsilon) be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X (epsilon) is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient: , X (0) = x, where B is an mxm matrix valued Brownian motion and B' denotes the transpose of the matrix B. In this paper, we prove that satisfies a large deviation principle, and converges to a Gaussian process, where h(E >) -> +a and as epsilon -> 0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X (epsilon) are also obtained by the delta method.