aeDensity function

Asymptotic Expansion - Density

aeDensity(..., ae, eps = 1, order = NULL)

Arguments

• ...: named argument, data.frame, list, or environment specifying the grid to evaluate the density. See examples.
• ae: an object of class yuima.ae-class.
• eps: numeric. The intensity of the perturbation.
• order: integer. The expansion order. If NULL (default), it uses the maximum order used in ae.

Returns

Probability density function evaluated on the given grid.

Examples

## Not run:

# model
gbm <- setModel(drift = 'mu*x', diffusion = 'sigma*x', solve.variable = 'x')

# settings
xinit <- 100
par <- list(mu = 0.01, sigma = 0.2)
sampling <- setSampling(Initial = 0, Terminal = 1, n = 1000)

# asymptotic expansion
approx <- ae(model = gbm, sampling = sampling, order = 4, true.parameter = par, xinit = xinit)

# The following are all equivalent methods to specify the grid via ....
# Notice that the character 'x' corresponds to the solve.variable of the yuima model.

# 1) named argument  
x <- seq(50, 200, by = 0.1)
density <- aeDensity(x = x, ae = approx, order = 4)
# 2) data frame
df <- data.frame(x = seq(50, 200, by = 0.1))
density <- aeDensity(df, ae = approx, order = 4)
# 3) environment
env <- new.env()
env$x <- seq(50, 200, by = 0.1)
density <- aeDensity(env, ae = approx, order = 4)
# 4) list
lst <- list(x = seq(50, 200, by = 0.1))
density <- aeDensity(lst, ae = approx, order = 4)

# exact density
exact <- dlnorm(x = x, meanlog = log(xinit)+(par$mu-0.5*par$sigma^2)*1, sdlog = par$sigma*sqrt(1))

# compare
plot(x = exact, y = density, xlab = "Exact", ylab = "Approximated")
## End(Not run)