# 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

## 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

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## Referenced By

The man pages GeneralizedOrnsteinUhlenbeckProcess(3) and level(3) are aliases of QuantLib_GeneralizedOrnsteinUhlenbeckProcess(3).

Wed Feb 7 2018 Version 1.10.1 QuantLib