DiffusionProcess Class Reference

#include <diffusionprocess.hpp>

Inheritance diagram for DiffusionProcess:

Inheritance graph
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List of all members.

Detailed Description

Diffusion process class.

This class describes a stochastic process governed by

\[ dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t. \]


Public Member Functions

 DiffusionProcess (double x0)
double x0 () const
virtual double drift (Time t, double x) const=0
 returns the drift part of the equation, i.e. $ \mu(t, x_t) $

virtual double diffusion (Time t, double x) const=0
 returns the diffusion part of the equation, i.e. $\sigma(t, x_t)$

virtual double expectation (Time t0, double x0, Time dt) const
 returns the expectation of the process after a time interval

virtual double variance (Time t0, double x0, Time dt) const
 returns the variance of the process after a time interval


Member Function Documentation

virtual double expectation Time  t0,
double  x0,
Time  dt
const [virtual]
 

returns the expectation of the process after a time interval

returns $ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $. By default, it returns the Euler approximation defined by $ x_0 + \mu(t_0, x_0) \Delta t $.

Reimplemented in OrnsteinUhlenbeckProcess.

virtual double variance Time  t0,
double  x0,
Time  dt
const [virtual]
 

returns the variance of the process after a time interval

returns $ Var(x_{t_0 + \Delta t} | x_{t_0} = x_0) $. By default, it returns the Euler approximation defined by $ \sigma(t_0, x_0)^2 \Delta t $.

Reimplemented in OrnsteinUhlenbeckProcess.


The documentation for this class was generated from the following file:

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