sde (version 2.0.9)

dcElerian: Approximated conditional law of a diffusion process by Elerian's method

Description

Approximated conditional densities for $X(t) | X(t_0) = x_0$ of a diffusion process.

Usage

dcElerian(x, t, x0, t0, theta, d, s, sx, log=FALSE)

Arguments

x

vector of quantiles.

t

lag or time.

x0

the value of the process at time t0; see details.

t0

initial time.

theta

parameter of the process; see details.

log

logical; if TRUE, probabilities $p$ are given as $\log(p)$.

d

drift coefficient as a function; see details.

s

diffusion coefficient as a function; see details.

sx

partial derivative w.r.t. x of the diffusion coefficient; see details.

Value

• x
  a numeric vector

Details

This function returns the value of the conditional density of $X(t) | X(t_0) = x_0$ at point x.

All the functions d, s, and sx must be functions of t, x, and theta.

References

Elerian, O. (1998) A note on the existence of a closed form conditional density for the Milstein scheme, Working Paper, Nuffield College, Oxford University. Available at http://www.nuff.ox.ac.uk/economics/papers/