A construction of processes with one dimensional martingale marginals, based upon path-space Ornstein-Uhlenbeck processes and the Brownian sheet
Francis Hirsch and Marc Yor
Source: J. Math. Kyoto Univ. Volume 49, Number 2 (2009), 389-417.
Abstract
Using a variation from the construction of the Ornstein-Uhlenbeck process on canonical path-space $C([0,1]; \mathbb{R})$ in terms of the Brownian sheet, we obtain a large class of processes, adapted to the Brownian filtration, which admit the one dimensional marginals of a martingale.
Primary Subjects: 60Gxx, 60Hxx
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Journal of Mathematics of Kyoto University
