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Methodology and Computing in Applied Probability

, Volume 18, Issue 3, pp 765–783 | Cite as

A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence

  • Enrico BibbonaEmail author
  • Laura Sacerdote
  • Emiliano Torre
Article

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 approach provides 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.

Keywords

Copulae Copulas Space-time transformations Diffusions Serial dependence Stochastic differential equations 

Mathematics Subject Classification (2010)

60J60 62M10 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics “G.Peano”University of TorinoTorinoItaly
  2. 2.Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA BRAIN Institute IJülich Research CentreJülichGermany
  3. 3.Department of Mathematical Sciences “G.L. Lagrange”Politecnico di TorinoTorinoItaly

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