sde (version 2.0.9)

dcKessler: Approximated conditional law of a diffusion process by Kessler's method

Description

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

Usage

dcKessler(x, t, x0, t0, theta, d, dx, dxx, s, sx, sxx, 
          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 wrt x^2 of the drift coefficient; see details.

s

diffusion coefficient as a function; see details.

sx

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

sxx

second partial derivative w.r.t. x^2 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, dx, dxx, dt, s, sx, and sxx must be functions of t, x, and theta.

References

Kessler, M. (1997) Estimation of an ergodic diffusion from discrete observations, Scand. J. Statist., 24, 211-229.