Multivariate Generalized Laplace Distributions and Related Random Fields

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails often observed in practical data, 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 basic properties of the latter distributions 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 and provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modelling potential of this construction. In memory of Professor Samuel Kotz