  This article is dedicated to the anisotropic sparse grid quadrature for
functions which are analytically extendable into an anisotropic tensor product
domain. Taking into account this anisotropy, we end up with a dimension
independent error versus cost estimate of the proposed quadrature. In addition,
we provide a novel and improved estimate for the cardinality of the underlying
anisotropic index set. To validate the theoretical findings, we present several
examples ranging from simple quadrature problems to diffusion problems on
random domains. These examples demonstrate the remarkable convergence behaviour
of the anisotropic sparse grid quadrature in applications.
