aeExpectation: Asymptotic Expansion - Functionals

In yuima: The YUIMA Project Package for SDEs

Asymptotic Expansion - Functionals

Description

Compute the expected value of functionals.

Usage

aeExpectation(f, bounds, ae, eps = 1, order = NULL, ...)

Arguments

f	character. The functional.
bounds	named list of integration bounds in the form list(x = c(xmin, xmax), y = c(ymin, ymax), ...)
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.
...	additional arguments passed to cubintegrate.

Value

return value of cubintegrate. The expectation of the functional provided.

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)

# compute the mean via integration
aeExpectation(f = 'x', bounds = list(x = c(0,1000)), ae = approx)

# compare with the mean computed by differentiation of the characteristic function
aeMean(approx)

## End(Not run)

yuima documentation built on April 16, 2025, 5:12 p.m.