U_ghuv: A dependence structure of 2 random variables.

View source: R/covariance_matrix.R

U_ghuvR Documentation

A dependence structure of 2 random variables.


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}))


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



self-similarity parameter of alpha stable random motion.


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


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 Aug. 27, 2022, 5:06 p.m.

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