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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Bibbona, E., Sacerdote, L. & Torre, E. A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence. Methodol Comput Appl Probab 18, 765–783 (2016). https://doi.org/10.1007/s11009-016-9487-6
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DOI: https://doi.org/10.1007/s11009-016-9487-6
Keywords
- Copulae
- Copulas
- Space-time transformations
- Diffusions
- Serial dependence
- Stochastic differential equations