29 lines
957 B
R
29 lines
957 B
R
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# Normal approximation of the density function of the Esscher
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# transform of a 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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#' Normal approximation of the density function of the
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#' Esscher transform of a Laplace Motion
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#' @param x vector of quantiles
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#' @param param Parameter vector
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#' @param hEsscher Esscher transform parameter
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#' @param eval.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 Normal density function approximation of the Esscher transform
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#' of the specified Laplace motion
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dnormapproxEsscherLM <- function(x,param,hEsscher=0,eval.time=1,type="mu",log=FALSE,start=0)
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{
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dnorm(x,start+eval.time*(mGAL(1,param,type,log)+hEsscher*cmGAL(2,param,type,log)),
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sqrt(eval.time*cmGAL(2,param,type,log)))
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}
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