sde (version 2.0.9)

dcShoji: Approximated conditional law of a diffusion process by the Shoji-Ozaki method

Description

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

Usage

dcShoji(x, t, x0, t0, theta, d, dx, dxx, dt, s, 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.

dx

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

dxx

second partial derivative w.r.t. x^2 of the drift coefficient; see details.

dt

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

s

diffusion coefficient as a function; 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, dx, dxx, dt, and s must be functions of t, x, and theta.

References

Shoji, L., Ozaki, T. (1998) Estimation for nonlinear stochastic differential equations by a local linearization method, Stochastic Analysis and Applications, 16, 733-752.