Series Representations for Multivariate Generalized Gamma Processes via a Scale Invariance Principle
نویسندگان
چکیده
We introduce a scale invariance property for Poisson point processes and use this property to define a series representation for a correlated bivariate gamma process. This approach is quite general and can be used to define other types of multidimensional Lévy processes with given marginals. Some important special cases are bivariate G-processes, bivariate variance gamma processes and multivariate Dirichlet processes. Using the scale invariance principle we show how to construct simple approximations to these multivariate processes.
منابع مشابه
Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes
The problem of simulation of multivariate Lévy processes is investigated. A method based on generalized shot noise series representations of Lévy processes combined with Gaussian approximation of the remainder is established in full generality. This method is applied to multivariate stable and tempered stable processes and formulas for their approximate simulation are obtained. Key-words: Lévy ...
متن کاملOn the Asymptotic Behavior of Generalized Processes, with Applications to Nonlinear Evolution Equations
The invariance principle, introduced by LaSalle [40] and subsequentlygeneralized by Hale [34], gives information on the structure of w-limit sets in dynamical systems possessing a Liapunov function, and the principle and related methods have been used to determine the asymptotic behavior of solutions to a wide variety of evolution equations (see Kefs. [4, 10, 17-19, 23-29, 34, 48, 51, 55, 561)....
متن کاملNonequilibrium Thermodynamics and Scale Invariance
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown...
متن کاملGeneralized Laguerre expansions of multivariate probability densities with moments
We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an appr...
متن کاملLearning Discrete Representations via Information Maximizing Self-Augmented Training
Learning discrete representations of data is a central machine learning task because of the compactness of the representations and ease of interpretation. The task includes clustering and hash learning as special cases. Deep neural networks are promising to be used because they can model the non-linearity of data and scale to large datasets. However, their model complexity is huge, and therefor...
متن کامل