# level (3) - Linux Man Pages

### level: Ornstein-Uhlenbeck process class.

## NAME

QuantLib::OrnsteinUhlenbeckProcess - Ornstein-Uhlenbeck process class.

## SYNOPSIS

#include <ql/processes/ornsteinuhlenbeckprocess.hpp>

Inherits **QuantLib::StochasticProcess1D**.

### Public Member Functions

**OrnsteinUhlenbeckProcess** (Real speed, **Volatility** vol, Real x0=0.0, Real level=0.0)

**StochasticProcess interface**

Real **x0** () const

*returns the initial value of the state variable *

Real **speed** () const

Real **volatility** () const

Real **level** () const

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. $ igma(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

Ornstein-Uhlenbeck process class.

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

## 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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