Multivariate Escher Transformed Laplace Distribution and Its Generalization

Abstract

This paper we introduced a new distribution namely the multivariate Esscher transformed Laplace distribution. Various properties of the distribution are studied and the applications are discussed. Further we develop an autoregressive process with multi-variateETLmarginalandstudyitsproperties.ALevyprocessbasedonthismultivariateinfinitelydivisibledistributionisknown as Laplace motion, and its marginal distributions are multivariate generalized Esscher transformed Laplace distribution.