On Copula-Itô processes

IF 0.6 Q4 STATISTICS & PROBABILITY

Dependence Modeling Pub Date : 2019-01-01 DOI:10.1515/demo-2019-0017

P. Jaworski

引用次数: 1

Abstract

Abstract We study the dynamics of the family of copulas {Ct}t≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H1 (ℝ2)* we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → Ct. Furthermore we show that the family {Ct}t≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup.

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关于Copula Itô过程

摘要我们研究了交配科的动力学{Ct}t由随机微分方程（SDE）给出的一对随机过程的≥0。我们把它与一个抛物型偏微分方程联系起来。在Sobolev Hilbert空间H1的对偶中嵌入了一组二元连接词(ℝ2） *我们计算关于t的导数和*弱拓扑，即曲线t图像的切向量场→ Ct.此外，我们还表明{Ct}t≥0是强连续变换半群的一个轨道，并提供了该半群的无穷小生成元。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Dependence Modeling STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 weeks

期刊介绍： The journal Dependence Modeling aims at providing a medium for exchanging results and ideas in the area of multivariate dependence modeling. It is an open access fully peer-reviewed journal providing the readers with free, instant, and permanent access to all content worldwide. Dependence Modeling is listed by Web of Science (Emerging Sources Citation Index), Scopus, MathSciNet and Zentralblatt Math. The journal presents different types of articles: -"Research Articles" on fundamental theoretical aspects, as well as on significant applications in science, engineering, economics, finance, insurance and other fields. -"Review Articles" which present the existing literature on the specific topic from new perspectives. -"Interview articles" limited to two papers per year, covering interviews with milestone personalities in the field of Dependence Modeling. The journal topics include (but are not limited to):　 -Copula methods -Multivariate distributions -Estimation and goodness-of-fit tests -Measures of association -Quantitative risk management -Risk measures and stochastic orders -Time series -Environmental sciences -Computational methods and software -Extreme-value theory -Limit laws -Mass Transportations