%0 Journal Article
%T A copula-based method to build diffusion models with prescribed marginal and serial dependence
%A Enrico Bibbona
%A Laura Sacerdote
%A Emiliano Torre
%J Statistics
%D 2015
%I arXiv
%X This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This provides us a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models. A possible application in neuroscience is sketched as a proof of concept.
%U http://arxiv.org/abs/1509.02319v2