dev.nm.stat.stochasticprocess.multivariate.sde.discrete

Class MultivariateBrownianSDE

java.lang.Object

dev.nm.stat.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.

See Also:

"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

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