com.numericalmethod.suanshu.stats.stochasticprocess.univariate.brownian
Class Brownian

java.lang.Object
  com.numericalmethod.suanshu.stats.stochasticprocess.univariate.brownian.Brownian

All Implemented Interfaces:

DiscretizedSDE

Direct Known Subclasses:

RandomWalk

public class Brownian
extends java.lang.Object
implements DiscretizedSDE

A 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 normally distributed with mean 0 and variance (t - s).

See Also:

"Fima C. Klebaner. Introduction to Stochastic Calculus with Applications. 2nd ed. Section 3.1. Imperial College Press. 2006."

Field Summary

double	mu μ, the drift
double	sigma σ, the diffusion constant

Constructor Summary

Brownian()
Construct a univariate standard Brownian motion.

Brownian(double mu, double sigma)
Construct a univariate Brownian motion.

Method Summary

double	dXt(Ft ft) This is the SDE specification of the stochastic process.
Ft	getNewFt() Get an empty filtration for the process.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

mu

public final double mu

μ, the drift

sigma

public final double sigma

σ, the diffusion constant

Constructor Detail

Brownian

public Brownian(double mu,
                double sigma)

Construct a univariate Brownian motion.

Parameters:

mu - μ, the drift

sigma - σ, the diffusion constant

Brownian

public Brownian()

Construct a univariate standard Brownian motion.

Method Detail

dXt

public double dXt(Ft ft)

Description copied from interface: DiscretizedSDE

This is the SDE specification of the stochastic process.

Specified by:

dXt in interface DiscretizedSDE

Parameters:

ft - filtration

Returns:

the increment of the process in dt

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