LARGE DEVIATIONS FOR WISHART PROCESSES
Abstract: Let be a Wishart process of dimension , with values in the set of positive
matrices of size . We are interested in the large deviations for a family of matrix-valued
processes as tends to infinity. The process is a solution of a
stochastic differential equation with a degenerate diffusion coefficient. Our approach is based
upon the introduction of exponential martingales. We give some applications to large
deviations for functionals of the Wishart processes, for example the set of eigenvalues.
2000 AMS Mathematics Subject Classification: 60F10, 60J60, 15A52.
Keywords and phrases: Wishart processes, large deviation principle.