dcShoji: Approximated conditional law of a diffusion process by the...

In sde: Simulation and Inference for Stochastic Differential Equations

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

Description

Approximated conditional densities for X(t) | X(t0) = x0 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.

Details

This function returns the value of the conditional density of X(t) | X(t0) = x0 at point x.

All the functions d, dx, dxx, dt, and s must be functions of t, x, and theta.

Value

x	a numeric vector

Author(s)

Stefano Maria Iacus

References

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

sde documentation built on Sept. 9, 2022, 3:07 p.m.