/*! Returns an approximation of the covariance defined as
* \f$ \sigma(t_0, \mathbf{x}_0)^2 \Delta t \f$. */
public Matrix covariance(StochasticProcess process, double t0, Vector x0, double dt)
{
Matrix sigma = process.diffusion(t0, x0);
Matrix result = sigma * Matrix.transpose(sigma) * dt;
return(result);
}
/*! Returns an approximation of the diffusion defined as
\f$ \sigma(t_0, \mathbf{x}_0) \sqrt{\Delta t} \f$. */
public Matrix diffusion(StochasticProcess process, double t0, Vector x0, double dt)
{
return process.diffusion(t0, x0) * Math.Sqrt(dt);
}
/*! Returns an approximation of the diffusion defined as
* \f$ \sigma(t_0, \mathbf{x}_0) \sqrt{\Delta t} \f$. */
public Matrix diffusion(StochasticProcess process, double t0, Vector x0, double dt)
{
return(process.diffusion(t0, x0) * Math.Sqrt(dt));
}
/*! Returns an approximation of the covariance defined as
\f$ \sigma(t_0, \mathbf{x}_0)^2 \Delta t \f$. */
public Matrix covariance(StochasticProcess process, double t0, Vector x0, double dt)
{
Matrix sigma = process.diffusion(t0, x0);
Matrix result = sigma * Matrix.transpose(sigma) * dt;
return result;
}