GaussMarkovProcess Class Reference

Implementation of a stationary gauss-markov process, also known as a Ornstein Ulenbeck process. More...

#include <gz/math/GaussMarkovProcess.hh>

Public Member Functions
	GaussMarkovProcess ()
	GaussMarkovProcess (double _start, double _theta, double _mu, double _sigma)
	Create a process with the provided process parameters. This will also call Set(), and in turn Reset().
double	Mu () const
	Get the mu ( \(\mu\)) value.
void	Reset ()
	Reset the process. This will set the current process value to the start value.
void	Set (double _start, double _theta, double _mu, double _sigma)
	Set the process parameters. This will also call Reset().
double	Sigma () const
	Get the sigma ( \(\sigma\)) value.
double	Start () const
	Get the start value.
double	Theta () const
	Get the theta ( \(\theta\)) value.
double	Update (const clock::duration &_dt)
	Update the process and get the new value.
double	Update (double _dt)
double	Value () const
	Get the current process value.

Detailed Description

Implementation of a stationary gauss-markov process, also known as a Ornstein Ulenbeck process.

See the Update(const clock::duration &) for details on the forumla used to update the process.

Example usage

#include <iostream>
#include <gz/math/GaussMarkovProcess.hh>
 
// You can plot the data generated by this program by following these
// steps.
//
// 1. Run this program and save the output to a file:
//     ./gauss_markov_process > plot.data
//
// 2. Use gnuplot to create a plot:
//     gnuplot -e 'set terminal jpeg; plot "plot.data" with lines' > out.jpg
int main(int argc, char **argv)
{
  // Create the process with:
  //   * Start value of 20.2
  //   * Theta (rate at which the process should approach the mean) of 0.1
  //   * Mu (mean value) 0.
  //   * Sigma (volatility) of 0.5.
  gz::math::GaussMarkovProcess gmp(20.2, 0.1, 0, 0.5);
 
  std::chrono::steady_clock::duration dt = std::chrono::milliseconds(100);
 
  // This process should decrease toward the mean value of 0.
  // With noise of 0.5, the process will walk a bit.
  for (int i = 0; i < 1000; ++i)
  {
    double value = gmp.Update(dt);
    std::cout << value << std::endl;
  }
 
  return 0;
}

Constructor & Destructor Documentation

GaussMarkovProcess() [1/2]

GaussMarkovProcess

(

)

GaussMarkovProcess() [2/2]

GaussMarkovProcess	(	double	_start,
		double	_theta,
		double	_mu,
		double	_sigma
	)

Create a process with the provided process parameters. This will also call Set(), and in turn Reset().

Parameters

[in]	_start	The start value of the process.
[in]	_theta	The theta ( \(\theta\)) parameter. A value of zero will be used if this parameter is negative.
[in]	_mu	The mu ( \(\mu\)) parameter.
[in]	_sigma	The sigma ( \(\sigma\)) parameter. A value of zero will be used if this parameter is negative.

See also

Update(const clock::duration &)

Member Function Documentation

Mu()

double Mu

(

)

const

Get the mu ( \(\mu\)) value.

Returns

The mu value.

See also

Set(double, double, double, double)

Reset()

void Reset

(

)

Reset the process. This will set the current process value to the start value.

Set()

void Set	(	double	_start,
		double	_theta,
		double	_mu,
		double	_sigma
	)

Set the process parameters. This will also call Reset().

Parameters

[in]	_start	The start value of the process.
[in]	_theta	The theta ( \(\theta\)) parameter.
[in]	_mu	The mu ( \(\mu\)) parameter.
[in]	_sigma	The sigma ( \(\sigma\)) parameter.

See also

Update(const clock::duration &)

Sigma()

double Sigma

(

)

const

Get the sigma ( \(\sigma\)) value.

Returns

The sigma value.

See also

Set(double, double, double, double)

Start()

double Start

(

)

const

Get the start value.

Returns

The start value.

See also

Set(double, double, double, double)

Theta()

double Theta

(

)

const

Get the theta ( \(\theta\)) value.

Returns

The theta value.

See also

Set(double, double, double, double)

Update() [1/2]

double Update

(

const clock::duration &

_dt

)

Update the process and get the new value.

The following equation is computed:

\(x_{t+1} += \theta * (\mu - x_t) * dt + \sigma * dW_t\)

where

• \(\theta, \mu, \sigma\) are parameters specified by the user. In order, the parameters are theta, mu, and sigma. Theta and sigma must be greater than or equal to zero. You can think of mu as representing the mean or equilibrium value, sigma as the degree of volatility, and theta as the rate by which changes dissipate and revert towards the mean.
• \(dt\) is the time step in seconds.
• \(dW_t\) is a random number drawm from a normal distribution with mean of zero and variance of 1.
• \(x_t\) is the current value of the Gauss-Markov process
• \(x_{t+1}\) is the new value of the Gauss-Markvov process

See also: https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process

This implementation include a drift parameter, mu. In financial mathematics, this is known as a Vasicek model.

Parameters

[in]

_dt

Length of the timestep after which a new sample should be taken.

Returns

The new value of this process.

Update() [2/2]

double Update

(

double

_dt

)

Value()

double Value

(

)

const

Get the current process value.

Returns

The value of the process.

---

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

• GaussMarkovProcess.hh