Estimate the Hurst parameter of a plane indexed fractional Brownian field by the quadratic variations method

Description

The function quadvar yields the estimation of the Hurst parameter of a fractional Brownian field by the quadratic variations method in the plane case.

Usage

quadvar(process,parameter)

Arguments

Details

The Hurst parameter of the fractal Brownian field is estimated by the procedure described in Istas and Lang (1997).

Value

Author(s)

Alexandre Brouste (http://perso.univ-lemans.fr/~abrouste/) and Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/).

References

J. Istas and G. Lang (1997). Quadratic variations and estimation of the local Holder index of a Gaussian process. Annales Institut Henri Poincare, 33,407-436.

See Also

fieldsim, setProcess, setValues.

Examples

# load FieldSim library
library(FieldSim)

# Simulated Fractional Brownian field on [0,1]^2
plane.fBm<-setProcess("fBm-plane",0.7)
fieldsim(plane.fBm)
quadvar(plane.fBm)

# Simulated Multifractional Brownian field on [0,1]^2
funcH<-function(xi){0.3+xi[1]*0.6}
plane.mBm<-setProcess("mBm-plane",funcH)
fieldsim(plane.mBm)
quadvar(plane.mBm,parameter=list(point=c(0.5,0.5),h=0.2))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(FieldSim)
Loading required package: rgl
Loading required package: RColorBrewer
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FieldSim/quadvar.Rd_%03d_medium.png", width=480, height=480)
> ### Name: quadvar
> ### Title: Estimate the Hurst parameter of a plane indexed fractional
> ###   Brownian field by the quadratic variations method
> ### Aliases: quadvar
> 
> ### ** Examples
> 
> # load FieldSim library
> library(FieldSim)
> 
> # Simulated Fractional Brownian field on [0,1]^2
> plane.fBm<-setProcess("fBm-plane",0.7)
> fieldsim(plane.fBm)
> quadvar(plane.fBm)
[1] 0.3709428
> 
> # Simulated Multifractional Brownian field on [0,1]^2
> funcH<-function(xi){0.3+xi[1]*0.6}
> plane.mBm<-setProcess("mBm-plane",funcH)
> fieldsim(plane.mBm)
> quadvar(plane.mBm,parameter=list(point=c(0.5,0.5),h=0.2))
[1] 0.1412386
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>