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 Publish in OALib Journal ISSN: 2333-9721 APC: Only $99  Views Downloads  Relative Articles Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices Large deviations for renewal processes Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble A unified approach for large deviations of bulk and extreme eigenvalues of the Wishart ensemble Large deviations for Markov processes with resetting Wishart Processes Large deviations for processes with discontinuous statistics Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices Large Deviations for a Non-Centered Wishart Matrix Large deviations of Poisson cluster processes More... Mathematics 2004 # Large deviations for Wishart processes  Full-Text Cite this paper Abstract: Let$X^{(\delta)}$be a Wishart process of dimension$\delta$, with values in the set of positive matrices of size$m$. We are interested in the large deviations for a family of matrix-valued processes$\{\delta^{-1} X_t^{(\delta)}, t \leq 1 \}$as$\delta$tends to infinity. The process$X^{(\delta)}\$ 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.

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