Welehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate \ell_1-norm symmetric distributions. Building upon their results, we } introduce a class of multivariate Markov processes that we call `Archimedean survival processes' (ASPs) and present some of their properties. An ASP is defined over a finite time horizon and,a priori , its terminal value has an \ell_1-norm symmetric distribution and an Archimedean survival copula . Indeed, there is a bijection between the class of Archimedean copulas and the class of ASPs . The finite-dimensional distributions of an ASP are of multivariate Liouville-type. The one-dimensional marginal processes are so-called gamma random bridges (that is, each marginal is the product of gamma bridge with an independent positive random variable). These marginal processes are increasing and, in general, not independent, but they are identical in law. The law of an n-dimensional ASP is equivalent to that of an n-dimensional gamma process, and we provide details of the associated change of measure. The law an n-dimensional ASP is identical to the law of a positive random variable multiplied by the Hadamard product of an n-dimensional Dirichlet random variable and a vector of n independent gamma bridges. We generalise ASPs to a family of stochastic processes that we call `Liouville processes.' A Liouville process is also a multivariate Markov process whose finite-dimensional distributions are multivariate Liouville. However, in general, the terminal value of a Liouville process does not have an Archimedean survival copula, and its one-dimensional marginal processes are not identical in law .
Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. A. J. McNeil and J. Ne\v{slehov\'a (2009) showed that the class of Archimedean copulas coincides with the class of multivariate \ell_1-norm symmetric distributions. Building upon their results, we } introduce a class of multivariate Markov processes that we call `Archimedean survival processes' (ASPs) . The terminal value of an ASP has an Archimedean survival copula , and there exists a bijection from the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation .
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Archimedean copulas and the class of ASPs . The finite-dimensional distributions of an ASP are of multivariate Liouville-type. The one-dimensional marginal processes are so-called gamma random bridges (that is, each marginal is the product of gamma bridge with an independent positive random variable). These marginal processes are increasing and, in general, not independent, but they are identical in law. The law of an n-dimensional ASP is equivalent to that of an n-dimensional gamma process, and we provide details of the associated change of measure. The law an n-dimensional ASP is identical to the law of a positive random variable multiplied by the Hadamard product of an n-dimensional Dirichlet random variable and a vector of n independent gamma bridges. We generalise ASPs to a family of stochastic processes that we call `Liouville processes.' A Liouville process is also a multivariate Markov process whose finite-dimensional distributions are multivariate Liouville. However, in general, the terminal value of a Liouville process does not have an Archimedean survival copula, and its one-dimensional marginal processes are not identical in law
ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation