Canonical decomposition of Gaussian measures in Banach spaces

par M. Jean-Charles Croix (EMSE)

jeudi 13 avr. 2017, 14:00 → 15:00 Europe/Paris

( C112, rez-de-chaussée bâtiment C, Université Jean Monnet St-Étienne - La Métare ) (UJM)

The study of Gaussian measures in Banach spaces is important both in pure and applied mathematics. In particular, their decomposition is of practical interest. In this paper, we show that every Gaussian measure on a separable Banach space can be decomposed in a constructive manner, based on a decomposition of the associated covariance operator. In particular, this can be interpreted as an extension of the spectral theorem to Gaussian covariances in Banach spaces. Finally, in the special case of the Wiener standard measure, this decomposition matches with Paul Levy's construction.