returns the expectation $$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
returns the number of independent factors of the process
returns the time value corresponding to the given date in the reference system of the stochastic process.
note As a number of processes might not need this functionality, a default implementation is given which raises an exception.
returns the variance $$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ of the process after a time interval $ \Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.
Geman-Roncoroni process class
This class describes the Geman-Roncoroni process governed by $$ \begin{array}{rcl} dE(t) &=& \left[ \frac{\partial}{\partial t} \mu(t) +\theta_1 \left(\mu(t)-E(t^-)\right)\right]dt +\sigma dW(t) + h(E(t^-))dJ(t) \ \mu(t)&=& \alpha + \beta t +\gamma \cos(\epsilon+2\pi t) +\delta \cos(\zeta + 4\pi t) \end{array} $$