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New results on Squared Bessel particle systems and Wishart processes

Hold Date 2018-05-18 16:30~2018-05-18 18:00

Place Seminar Room W1-D-725, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Piotr GRACZYK (Université d'Angers)

We study the existence, uniqueness, collisions  and other properties of Squared Bessel particle systems in full generality, i.e. admitting that they take also negative values. We extend the results obtained by Going-Jaeschke and Yor in 1-dimensional case. Squared Bessel particle systems may be interpreted as eigenvalues of Wishart processes. We determine the parameter set of Wishart processes, i.e. the stochastic Gindikin set and deduce the first characterization of analytical non-central Gindikin set. Our techniques use elementary symmetric polynomials and, for Wishart processes, the theory of affine stochastic processes. (joint work with J. Malecki and E. Mayerhofer)