A copula-based method to build diffusion models with prescribed marginal and serial dependence
Abstract
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.
Cite
@article{arxiv.1509.02319,
title = {A copula-based method to build diffusion models with prescribed marginal and serial dependence},
author = {Enrico Bibbona and Laura Sacerdote and Emiliano Torre},
journal= {arXiv preprint arXiv:1509.02319},
year = {2015}
}