# SuanShu, a Java numerical and statistical library

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

## Class MultivariateBrownianSDE

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

public class MultivariateBrownianSDE
extends Object
implements MultivariateDiscreteSDE
A multivariate Brownian motion is a stochastic process with the following properties.
• B(0) = 0;
• B(t), t >= 0, are continuous functions of t;
• the increments, B(t) - B(s), t > s, are independent of the past;
• the increments, B(t) - B(s), are (correlated) multi- normally distributed with mean 0.
"Fima C. Klebaner, "Section 3.1," Introduction to Stochastic Calculus with Applications, 2nd ed, Imperial College Press, 2006."
• ### Constructor Summary

Constructors
Constructor and Description
MultivariateBrownianSDE(int d)
Construct a standard multi-dimensional Brownian motion.
MultivariateBrownianSDE(Vector mu, Matrix sigma)
Construct a multi-dimensional Brownian motion.
• ### 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

• #### MultivariateBrownianSDE

public MultivariateBrownianSDE(int d)
Construct a standard multi-dimensional Brownian motion.
Parameters:
d - the dimension
• #### MultivariateBrownianSDE

public MultivariateBrownianSDE(Vector mu,
Matrix sigma)
Construct a multi-dimensional Brownian motion.
Parameters:
mu - μ
sigma - σ
• ### Method Detail

• #### dXt

public Vector dXt(MultivariateFt ft)
Description copied from interface: MultivariateDiscreteSDE
This is the SDE specification of a stochastic process.
Specified by:
dXt in interface MultivariateDiscreteSDE
Parameters:
ft - 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