2014-02-14 04:46:32 +00:00
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# Characteristic function of Laplace motion
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Characteristic function of Laplace motion
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#' @param u Transform variate
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#' @param param Parameter vector
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#' @param time Time of the process
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#' @param type Choose between "mu" or "kappa" parametrization
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#' @param log Logical for log-parameters
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#' @param start Starting value of the process
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#' @return Characteristic function value at point u for given parameter vector
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#'
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#' @author Francois Pelletier
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2014-02-16 21:48:40 +00:00
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cfLM <- function(u,param,time=1,type="mu",log=FALSE,start=0)
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2014-02-14 04:46:32 +00:00
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{
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testparGAL(param,type,log)
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if(log)
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{
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if(type=="mu")
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{
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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)
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}
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if(type=="kappa")
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{
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exp(1i*(start+exp(param[1])*time)*u)*(1+(exp(param[2])^2*u^2)/2-(1/2*1i)*
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exp(param[2])*sqrt(2)*(1/exp(param[3])-exp(param[3]))*u)^(-exp(param[4])*time)
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}
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}
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else
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{
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if(type=="mu")
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{
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exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-1i*param[3]*u)^(-param[4]*time)
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}
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if(type=="kappa")
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{
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exp(1i*(start+param[1]*time)*u)*(1+(param[2]^2*u^2)/2-(1/2*1i)*
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param[2]*sqrt(2)*(1/param[3]-param[3])*u)^(-param[4]*time)
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}
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}
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}
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