# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.sde.discrete

## Class MultivariateEulerSDE

• java.lang.Object
• com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.sde.discrete.MultivariateEulerSDE
• All Implemented Interfaces:
MultivariateDiscreteSDE

public class MultivariateEulerSDE
extends Object
implements MultivariateDiscreteSDE
The Euler scheme is the first order approximation of an SDE. $dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t$
Wikipedia: Euler-Maruyama method
• ### Constructor Summary

Constructors
Constructor and Description
MultivariateEulerSDE(MultivariateSDE sde)
Discretize a multivariate, continuous-time SDE using the Euler scheme.
• ### Method Summary

All Methods
Modifier and Type Method and Description
Vector dXt(MultivariateFt ft)
This is the SDE specification of a stochastic process.
MultivariateFt getNewFt()
Get an empty filtration of the process.
int nB()
Get the number of independent driving Brownian motions.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### MultivariateEulerSDE

public MultivariateEulerSDE(MultivariateSDE sde)
Discretize a multivariate, continuous-time SDE using the Euler scheme.
Parameters:
sde - a continuous-time SDE
• ### Method Detail

• #### dXt

public Vector dXt(MultivariateFt ft)
This is the SDE specification of a stochastic process.

$$dX_t = \mu * dt + \sigma * \sqrt{dt} * Z_t$$

Specified by:
dXt in interface MultivariateDiscreteSDE
Parameters:
ft - a filtration
Returns:
the increment of the process in dt
• #### nB

public int nB()
Description copied from interface: MultivariateDiscreteSDE
Get the number of independent driving Brownian motions.
Specified by:
nB in interface MultivariateDiscreteSDE
Returns:
the number of independent driving Brownian motions
• #### getNewFt

public MultivariateFt getNewFt()
Description copied from interface: MultivariateDiscreteSDE
Get an empty filtration of the process.
Specified by:
getNewFt in interface MultivariateDiscreteSDE
Returns:
an empty filtration