dcShoji function

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

Approximated conditional densities for $X(t) | X(t0) = x0$ of a diffusion process.

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.

Returns

• 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.