fracsim.1d {FracSim}R Documentation

Simulation of 1D fractional and multifractional Lévy motions

Description

The function simulates 1D fractional and multifractional motions

Usage

fracsim.1d(h, n, k, m = 1)

Arguments

h Regularity function. One value for fractional motions; either a function or a vector of length k for multifractional ones
n Number of terms in the serie
k Either the vector of discretisation points or the number of discretisation points (calculated equally spaced)
m Mass term, usually set equal to 1

Value

t k-vector of discretization points
simul.h Vector of simulated regularity values
process k-vector which elements are the process value at each discretization point

Author(s)

Sébastien Déjean & Serge Cohen

References

http://www.lsp.ups-tlse.fr/FracSim

See Also

fracsim.2d

Examples

library(FracSim)
# Fractional process
X05 = fracsim.1d(h=0.5,k=1000,n=5000)
plot(X05$t,X05$process,type="l")
# Multifractional process
# h is a k-vector
Hsin = 0.25+0.25*sin(seq(0,1,length=1000)*(6*pi))
Xsin = fracsim.1d(h=Hsin,k=1000,n=5000)
plot(Xsin$t,Xsin$process,type="l")
sint=function(x){0.5+0.5*sin(6*pi*x)}
# h is a function
Xsin2=fracsim.1d(sint,1000,500,1)
par(mfrow=c(2,1))
plot(Xsin2$t,Xsin2$simul.h,type="l")
plot(Xsin2$t,Xsin2$process,type="l")
par(mfrow=c(1,1))

[Package FracSim version 0.3 Index]