# ExtendedOrnsteinUhlenbeckProcess

## NAME

ExtendedOrnsteinUhlenbeckProcess ā Extended Ornstein-Uhlenbeck process class.

## SYNOPSIS

`#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>`

Inherits **StochasticProcess1D**.

**Public Types**

enum **Discretization** { **MidPoint**, **Trapezodial**, **GaussLobatto** }

**Public Member Functions**

**ExtendedOrnsteinUhlenbeckProcess** (**Real** speed, **Volatility** sigma, **Real x0**, const boost::function< **Real**(**Real**)> &b, Discretization **discretization**=MidPoint, **Real** intEps=1eā4)

**StochasticProcess interface**

**Real x0** () const

returns the initial value of the state variable

Real speed () const

Real volatility () const

Real drift (**Time** t, **Real** x) const

returns the drift part of the equation, i.e. $ (t, x_t) $

Real diffusion (**Time** t, **Real** x) const

returns the diffusion part of the equation, i.e. $ ma(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

Extended Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by dx = a (b(t) - x_t) dt + ma dW_t. ]

## Member Function Documentation

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

returns the expectation $ E(x_{t_0 + process after a time interval $ 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 + process after a time interval $ 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 + process after a time interval $ 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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