Multivariate generalized Laplace distributions and related random fields

In English Multivariate Laplace distribution is an important stochastic model that accounts for
asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second
moments. A Lévy process based on this multivariate infinitely divisible distribution is
known as Laplace motion, and its marginal distributions are multivariate generalized
Laplace laws. We review their basic properties and discuss a construction of a class of
moving average vector processes driven by multivariate Laplace motion. These stochastic
models extend to vector fields, which are multivariate both in the argument and the
value. They provide an attractive alternative to those based on Gaussianity, in presence
of asymmetry and heavy tails in empirical data. An example from engineering shows
modeling potential of this construction.