ae: Asymptotic Expansion

In yuima: The YUIMA Project Package for SDEs

Asymptotic Expansion

Description

Asymptotic expansion of uni-dimensional and multi-dimensional diffusion processes.

Usage

ae(
  model,
  xinit,
  order = 1L,
  true.parameter = list(),
  sampling = NULL,
  eps.var = "eps",
  solver = "rk4",
  verbose = FALSE
)

Arguments

model	an object of yuima-class or yuima.model-class.
xinit	initial value vector of state variables.
order	integer. The asymptotic expansion order. Higher orders lead to better approximations but longer computational times.
true.parameter	named list of parameters.
sampling	a yuima.sampling-class object.
eps.var	character. The perturbation variable.
solver	the solver for ordinary differential equations. One of "rk4" (more accurate) or "euler" (faster).
verbose	logical. Print on progress? Default FALSE.

Details

If sampling is not provided, then model must be an object of yuima-class with non-empty sampling.

if eps.var does not appear in the model specification, then it is internally added in front of the diffusion matrix to apply the asymptotic expansion scheme.

Value

An object of yuima.ae-class

Author(s)

Emanuele Guidotti <[e-mail]>

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)

# exact density
x <- seq(50, 200, by = 0.1)
exact <- dlnorm(x = x, meanlog = log(xinit)+(par$mu-0.5*par$sigma^2)*1, sdlog = par$sigma*sqrt(1))

# compare
plot(x, exact, type = 'l', ylab = "Density")
lines(x, aeDensity(x = x, ae = approx, order = 1), col = 2)
lines(x, aeDensity(x = x, ae = approx, order = 2), col = 3)
lines(x, aeDensity(x = x, ae = approx, order = 3), col = 4)
lines(x, aeDensity(x = x, ae = approx, order = 4), col = 5)

## End(Not run)

yuima documentation built on Nov. 14, 2022, 3:02 p.m.