Archimedean copulas are popular in the world of multivariate modelling as a result of their breadth, tractability, and flexibility. McNeil and Nešlehová (2009)  showed that the class of Archimedean copulas coincides with the class of positive multivariate ℓ1-norm symmetric distributions. Building upon their results, we introduce a class of multivariate Markov processes that we call 'Archimedean survival processes' (ASPs). An ASP is defined over a finite time interval, is equivalent in law to a vector of independent gamma processes, and its terminal value has an Archimedean survival copula. There exists a bijection from the class of ASPs to the class of Archimedean copulas. We provide various characterisations of ASPs, and a generalisation. © 2012 Elsevier Inc.
Hoyle, E., & Mengütürk, L. A. (2013). Archimedean survival processes. Journal of Multivariate Analysis, 115, 1–15. https://doi.org/10.1016/j.jmva.2012.09.008