GeneralizedAsymmetricLaplace/R/cfLM.R

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# Characteristic function of Laplace motion
#
# Author: Francois Pelletier
#
# LGPL 3.0
###############################################################################
#' Characteristic function of Laplace motion
#' @param u Transform variate
#' @param param Parameter vector
#' @param time Time of the process
#' @param type Choose between "mu" or "kappa" parametrization
#' @param log Logical for log-parameters
#' @param start Starting value of the process
#' @return Characteristic function value at point u for given parameter vector
#'
#' @author Francois Pelletier
cfLM <- function(u,param,time=1,type="mu",log=FALSE,start=0)
{
testparGAL(param,type,log)
if(log)
{
if(type=="mu")
{
exp(1i*(start+exp(param[1])*time)*u)*(1+(exp(param[2])^2*u^2)/2-1i*exp(param[3])*u)^(-exp(param[4])*time)
}
if(type=="kappa")
{
exp(1i*(start+exp(param[1])*time)*u)*(1+(exp(param[2])^2*u^2)/2-(1/2*1i)*
exp(param[2])*sqrt(2)*(1/exp(param[3])-exp(param[3]))*u)^(-exp(param[4])*time)
}
}
else
{
if(type=="mu")
{
exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-1i*param[3]*u)^(-param[4]*time)
}
if(type=="kappa")
{
exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-(1/2*1i)*
param[2]*sqrt(2)*(1/param[3]-param[3])*u)^(-param[4]*time)
}
}
}