  Pickands constants play a crucial role in the asymptotic theory of Gaussian
processes. They are commonly defined as the limits of a sequence of
expectations involving fractional Brownian motions and, as such, their exact
value is often unknown. Recently, Dieker and Yakir (2014) derived a novel
representation of Pickands constant as a simple expected value that does not
involve a limit operation. In this paper we show that the notion of Pickands
constants and their corresponding Dieker-Yakir representations can be extended
to a large class of stochastic processes, including general Gaussian and L\'evy
processes. We furthermore provide a link to spatial extreme value theory and
show that Pickands-type constants coincide with certain constants arising in
the study of max-stable processes with mixed moving maxima representations.
