dcKessler {sde}R Documentation

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

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 intial 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 wrt 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 wrt x of the diffusion coefficient. See details.
sxx second partial derivative wrt 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 t0, x0 and theta.

Value

x a numeric vector

Note

This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.

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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