returns the asset value after a time interval $ \Delta t $ according to the given discretization. By default, it returns $$ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w $$ where $ E $ is the expectation and $ S $ the standard deviation.
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 standard deviation $$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) $$ 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 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.
returns the initial value of the state variable
forward-measure 1-D stochastic process
1-D stochastic process whose dynamics are expressed in the forward measure.