# U_ghuv: A dependence structure of 2 random variables. In rlfsm: Simulations and Statistical Inference for Linear Fractional Stable Motions

## Description

It is used when random variables do not have finite second moments, and thus, the covariance matrix is not defined. For X= \int_{\R} g_s dL_s and Y= \int_{\R} h_s dL_s with \| g \|_{α}, \| h\|_{α}< ∞. Then the measure of dependence is given by U_{g,h}: \R^2 to \R via

U_{g,h} (u,v)=\exp(- σ^{α}{\| ug +vh \|_{α}}^{α} ) - \exp(- σ^{α} ({\| ug \|_{α}}^{α} + {\| vh \|_{α}}^{α}))

## Usage

 1 U_ghuv(alpha, sigma, g, h, u, v, ...) 

## Arguments

 alpha self-similarity parameter of alpha stable random motion. sigma Scale parameter of lfsm g, h functions g,h: \R to \R with finite alpha-norm (see Norm_alpha). v, u real numbers ... additional parameters to pass to U_gh and U_g

## Examples

 1 2 3 4 g<-function(x) exp(-x^2) h<-function(x) exp(-abs(x)) U_ghuv(alpha=1.5, sigma=1, g=g, h=h, u=10, v=15, rel.tol = .Machine\$double.eps^0.25, abs.tol=1e-11) 

rlfsm documentation built on April 16, 2021, 5:06 p.m.