Nothing
dcEuler <- function(x, t, x0, t0, theta, d, s, log=FALSE){
Dt <- t-t0
lik <- dnorm(x, mean = x0 + d(t0, x0, theta)*Dt, sd= sqrt(Dt)*s(t0,x0,theta),log=log)
lik[is.infinite(lik)] <- NA
lik
}
dcElerian <- function(x, t, x0, t0, theta, d, s, sx, log=FALSE){
Dt <- t-t0
A <- s(t0, x0, theta)*sx(t0, x0, theta)*Dt/2
B <- -s(t0, x0,theta)/(2*sx(t0, x0,theta)) + x0 + d(t0, x0, theta)*Dt - A
z <- (x-B)/A
z[z<0] <- NA
C <- 1/((s(t0, x0,theta)^2)*Dt)
tmp <- sqrt(C*z)
tmp2 <- numeric(length(tmp))
idx <- which(abs(tmp)>500)
tmp2[idx] <- tmp[idx] - log(2)
tmp2[-idx] <- log(cosh(tmp[-idx]))
lik <- -(C+z)/2 + tmp2 -0.5*log(z) - log(abs(A)) -log(2*pi)
if(!log)
lik <- exp(lik)
lik[is.infinite(lik)] <- NA
idx <- which(A==0)
lik[idx] <- dcEuler(x, t, x0, t0, theta, d, s, log)[idx]
lik
}
dcKessler <- function(x, t, x0, t0, theta, d, dx, dxx, s, sx, sxx, log=FALSE){
Dt <- t-t0
mu <- d(t0,x0,theta)
mu1 <- dx(t0,x0,theta)
mu2 <- dxx(t0,x0,theta)
sg <- s(t0,x0,theta)
sg1 <- sx(t0,x0,theta)
sg2 <- sxx(t0,x0,theta)
Ex <- (x0 + mu*Dt + (mu*mu1+0.5*(sg^2 * mu2))*(Dt^2)/2)
Vx <- ( x0^2 +(2*mu*x0 + sg^2)*Dt + (2*mu*(mu1*x0+mu+sg*sg1)+
sg^2*(mu2*x0 + 2*mu1 + sg1^2 + sg*sg2))*(Dt^2)/2 - Ex^2)
Vx[Vx<0] <- NA
dnorm(x, mean = Ex, sd=sqrt(Vx),log=log)
}
dcOzaki <- function(x, t, x0, t0, theta, d, dx, s, log=FALSE){
Dt <- t-t0
Lx <- dx(t0,x0,theta)
Kx <- log(1+d(t0,x0,theta)*(exp(Lx*Dt)-1)/(x0*Lx))/Dt
Ex <- x0 + d(t0,x0,theta)/Lx*(exp(Lx*Dt)-1)
Vx <- s(t0,x0,theta)^2 * (exp(2*Kx*Dt) -1)/(2*Kx)
dnorm(x, mean=Ex, sd=sqrt(Vx),log=log)
}
dcShoji <- function(x, t, x0, t0, theta, d, dx, dxx, dt, s, log=FALSE){
Dt <- t-t0
Lx <- dx(t0,x0,theta)
Mx <- s(t0,x0,theta)^2 * dxx(t0,x0,theta)/2 + dt(t0,x0,theta)
Ex <- (x0 + d(t0,x0,theta)*(exp(Lx*Dt)-1)/Lx +
Mx*(exp(Lx*Dt) -1 -Lx*Dt)/Lx^2)
Vx <- s(t0,x0,theta)^2*(exp(2*Lx*Dt)-1)/(2*Lx)
dnorm(x, mean=Ex, sd=sqrt(Vx),log=log)
}
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