dcOzaki: Approximated conditional law of a diffusion process by Ozaki's method
Description
Approximated conditional densities for $X(t) | X(t_0) = x_0$ of a diffusion process.
Usage
dcOzaki(x, t, x0, t0, theta, d, dx, 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.
s
diffusion coefficient as a function; see details.
Value
xa 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, and s must be functions of t, x, and theta.
References
Ozaki, T. (1992) A bridge between nonlinear time series models and
nonlinear stochastic dynamical systems: A local linearization approach,
Statistica Sinica, 2, 25-83.