機率研討會

主講者: Professor Si Si (Aichi Prefecture University)
講題: Quadratic Hida distributions and their applications
時間: 2009-03-24 (Tue.)  10:30 - 12:00
地點:
Abstract: Unitary representation of infinite symmetric group S(∞) appears in the study of Poisson noise. We defined an irreducible factor of a unitary representation of S(n) and applied the Bochner method in constructing the representation of S(∞) by taking projective limit. In the limit we can give a space of quadratic Hida distributions. Thus we can see the adjoint of the Levy Laplacian which naturally comes from Gaussian noise. In this sense, we can see a duality between two noises, Gaussian and Poisson. Gaussian and Poisson noises can be discussed not only in parallel, but we can see dissimilarity between them together with some interesting results by using the space of quadratic Hida distributions. Further we can discuss calculus of their functionals to see a duality of two noises.
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