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.

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

SACERDOTE, Laura Lea;
2016

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.
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http://arxiv.org/pdf/1509.02319.pdf
Copulas, Diffusion Processes; Space-time Transformations; Wiener Process
Bibbona E.; Sacerdote L.; Torre E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1557643
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