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Matrix-valued Bessel processes

Le : 27/05/2013 11h00
Par : Martin LARSSON, Swiss Finance Institute and EPFL (Suisse)
Lieu : I 103
Lien web :
Résumé : This talk discusses a matrix analog of the Bessel processes, taking values in the set E of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are obtained from the former via the map X -> X'X. The main focus is on existence and uniqueness, questions which lead us to develop several new results concerning the space of real square matrices. Specifically, certain powers of the determinant function are weight functions in the Muckenhoupt class; The set of matrices of co-rank at least two has zero capacity with respect to these weights; And for some powers, this even holds for the set of all singular matrices. As a consequence we obtain density results for Sobolev spaces over E with Neumann boundary conditions. The highly non-convex, non-Lipschitz structure of the state space is dealt with using the stratification of E into smooth manifolds consisting of fixed-rank matrices.