A local criterion for smoothness of densities and application to the supremum of the Brownian sheet (Q1344825)

The authors prove a criterion for the smoothness of the density for a once differentiable random variable taking values in an open subset of \(\text{Re}^ d\). As an application, it is shown that the maximum of the Brownian sheet on a rectangle \([0,s] \times [0,t]\) admits an infinitely differentiable density.