A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence
Methodology and Computing in Applied Probability(2016)
摘要
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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关键词
Copulae,Copulas,Space-time transformations,Diffusions,Serial dependence,Stochastic differential equations,60J60,62M10
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