com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian

Class Brownian

java.lang.Object

com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian.Brownian

All Implemented Interfaces:

DiscretizedSDE, java.io.Serializable

Direct Known Subclasses:

RandomWalk

public class Brownian
extends java.lang.Object
implements DiscretizedSDE

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. Introduction to Stochastic Calculus with Applications. 2nd ed. Section 3.1. Imperial College Press. 2006.", Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	d the dimension of this Brownian motion
Vector	mu μ, the drift
Matrix	sigma σ, the diffusion constant

Constructor Summary

Constructors

Constructor and Description
Brownian(int d) Construct a multi-dimensional Brownian motion.
Brownian(Vector mu, Matrix sigma) Construct a multi-dimensional Brownian motion with μ and σ.

Method Summary

Modifier and Type	Method and Description
Vector	dXt(Ft ft) This is the SDE specification of a stochastic process.
Ft	getNewFt() Get an empty filtration for 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

Field Detail

d

public final int d

the dimension of this Brownian motion

mu

public final Vector mu

μ, the drift

sigma

public final Matrix sigma

σ, the diffusion constant

Constructor Detail

Brownian

public Brownian(int d)

Construct a multi-dimensional Brownian motion.

Parameters:

d - the dimension

Brownian

public Brownian(Vector mu,
                Matrix sigma)

Construct a multi-dimensional Brownian motion with μ and σ.

Parameters:

mu - μ

sigma - σ

Method Detail

dXt

public Vector dXt(Ft ft)

Description copied from interface: DiscretizedSDE

This is the SDE specification of a stochastic process.

Specified by:

dXt in interface DiscretizedSDE

Parameters:

ft - filtration

Returns:

the increment of the process in dt

nB

public int nB()

Description copied from interface: DiscretizedSDE

Get the number of independent driving Brownian motions.

Specified by:

nB in interface DiscretizedSDE

Returns:

number of independent driving Brownian motions

getNewFt

public Ft getNewFt()

Description copied from interface: DiscretizedSDE

Get an empty filtration for the process.

Specified by:

getNewFt in interface DiscretizedSDE

Returns:

an empty filtration