On infinite dimensional sheets (Q1902483)

Let \(E\) be a Lusin space. The authors construct a Gaussian measure \(\mu\) on \({\mathcal C} (R^+, E)\), such that the coordinates \(W_{t,s}\) represent a generalized Brownian sheet (i.e. not vanishing on the axes). Then the generalized Ornstein-Uhlenbeck sheet is the solution of a stochastic linear partial differential system of Langevin type. The Cameron-Martin space is described with the use of four Gaussian measures. The process is stationary and Markovian when they are equal. Under a regularity hypothesis (R), this process has continuous trajectories and the associated capacity is defined and shown to be tight on compact sets. It gives a new way, after J. Bauer, to extend Song's results which says that the sets avoided by the bi-trajectories are the polar sets.