returns the covariance $$ V(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ 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 asset value after a time interval $\Delta$ according to the given discretization. By default, it returns $$ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} $$ where $E$ is the expectation and $S$ the standard deviation.
returns the expectation $$ E(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ 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 initial values of the state variables
returns the number of dimensions of the stochastic process
returns the standard deviation $$ S(\mathrm{x}{t_0 + \Delta t} | \mathrm{x}{t_0} = \mathrm{x}_0) $$ 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 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.
multi-dimensional stochastic process class
This class describes a stochastic process governed by:
$$ d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. $$