# QuantLib_GeneralizedOrnsteinUhlenbeckProcess man page

GeneralizedOrnsteinUhlenbeckProcess — Piecewise linear Ornstein-Uhlenbeck process class.

## Synopsis

`#include <ql/experimental/shortrate/generalizedornsteinuhlenbeckprocess.hpp>`

Inherits **StochasticProcess1D**.

### Public Member Functions

**GeneralizedOrnsteinUhlenbeckProcess** (const boost::function< **Real**(**Time**)> &speed, const boost::function< **Real**(**Time**)> &vol, **Real x0**=0.0, **Real** level=0.0)**Real speed** (**Time** t) const**Real volatility** (**Time** t) const**Real level** () const

**StochasticProcess1D interface**

**Real x0** () const

returns the initial value of the state variable **Real drift** (**Time** t, **Real** x) const

returns the drift part of the equation, i.e. $ mu(t, x_t) $ **Real diffusion** (**Time** t, **Real** x) const

returns the diffusion part of the equation, i.e. $ sigma(t, x_t) $ **Real expectation** (**Time** t0, **Real x0**, **Time** dt) const**Real stdDeviation** (**Time** t0, **Real x0**, **Time** dt) const**Real variance** (**Time** t0, **Real x0**, **Time** dt) const

### Additional Inherited Members

## Detailed Description

Piecewise linear Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by [ dx = a (level - x_t) dt + sigma dW_t ]

where the coefficients a and sigma are piecewise linear.

## Member Function Documentation

### Real expectation (Time t0, Real x0, Time dt) const [virtual]

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.

Reimplemented from **StochasticProcess1D**.

### Real stdDeviation (Time t0, Real x0, Time dt) const [virtual]

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.

Reimplemented from **StochasticProcess1D**.

### Real variance (Time t0, Real x0, Time dt) const [virtual]

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.

Reimplemented from **StochasticProcess1D**.

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

GeneralizedOrnsteinUhlenbeckProcess(3) and level(3) are aliases of QuantLib_GeneralizedOrnsteinUhlenbeckProcess(3).