Simulations of multivariate gamma distributions and multifactor gamma distributions

TL;DR

This paper develops a comprehensive framework for simulating multivariate gamma and multifactor gamma distributions, including algorithms for various dimensions and cases, enhancing the practical applicability of these distributions.

Contribution

It provides new algorithms for simulating infinitely divisible multivariate gamma distributions and their multifactor extensions across multiple dimensions.

Findings

Algorithms successfully simulate distributions in dimensions 2-5.

Explicit expressions for Laplace transforms of these distributions.

Demonstrations include simulations in multiple dimensions.

Abstract

This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma distributions.We give algorithms for simulating infinitely divisible gamma distributions and infinitely divisible multifactor gamma distributions in dimension 2,3,4 and for all dimensions greater than 2 in the Markovian case. We give examples of simulations in dimension 2,3,4 and in dimension 5 in the Markovian case.