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

Description

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

Usage

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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.

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, s, sx, and sxx must be functions of t, x, and theta.

Value

x

a numeric vector

Author(s)

Stefano Maria Iacus

References

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

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