Nothing
## ----eval=FALSE----------------------------------------------------------
# G1 <- function(t){-sin(2*pi*t)}
# Q0 <- function(t){1}
## ----eval=FALSE----------------------------------------------------------
# G1 <- function(t){-sin(2*pi*t)}
# Q0 <- function(t){1}
# Lam1 <- function(t){0.15}
# Jmu <- function(t){0.0}
# Jsig <- function(t){0.5}
## ----fig.align = 'center'------------------------------------------------
mu.x <- 0.1
sigma.x <- 0.5
lam <- 0.5
mu.z <- 0.1
sigma.z <- 0.5
true.density=function(X0,Xt,t,order =10)
{
dens <- exp(-lam*t)*dnorm(Xt,X0+mu.x*t,sqrt(sigma.x^2*t))
for(i in 1:order)
{
dens <- dens +exp(-lam*t)*(lam*t)^i/factorial(i)*dnorm(Xt,X0+mu.x*t+i*mu.z*t,sqrt(sigma.x^2*t+i*sigma.z^2*t))
}
return(list(density=dens,Xt=Xt))
}
Xt <- seq(-2,2,1/10)
res <- true.density(0,Xt,1)
plot(res$density~Xt,type='l',main='Transition Density',xlab='X_t',ylab='density')
## ----fig.align = 'center'------------------------------------------------
library(DiffusionRjgqd)
# Remove any existing coefficients:
JGQD.remove()
# Define the model coefficients:
G0 <- function(t){mu.x}
Q0 <- function(t){sigma.x^2}
Lam0 <- function(t){lam}
Jmu <- function(t){mu.z}
Jsig <- function(t){sigma.z}
# Calculate the transitional density:
BM <- JGQD.density(0,Xt,0,1,factorize=TRUE,Dtype='Normal.A')
# Plot the transitional density:
plot(res$density~Xt,type='l',main='Transition Density',xlab='X_t',ylab='density')
lines(BM$density[,100]~BM$Xt,col='blue',lty='dashed',lwd=2)
## ----eval=FALSE----------------------------------------------------------
# browseVignettes('DiffusionRjgqd')
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