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Seminar on Probability and Statistics
Seminar information archive ～11/21｜Next seminar｜Future seminars 11/22～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2018/05/23
14:00-15:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Lorenzo Mercuri (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
Lorenzo Mercuri (University of Milan)
"yuima.law": From mathematical representation of general Lévy processes to a numerical implementation
[ Abstract ]
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.
An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.
We present a new class called yuima.law that refers to the mathematical description of a general Lévy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Lévy process considered. This class creates a link between YUIMA and other R packages available on CRAN that manage specific Lévy processes.
An example of yuima.law is shown based the Mixed Tempered Stable(MixedTS) Lévy processes. A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated.
