# SuanShu, a Java numerical and statistical library

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

## Class BMSDE

• java.lang.Object
• com.numericalmethod.suanshu.stats.stochasticprocess.univariate.sde.discrete.BMSDE
• All Implemented Interfaces:
DiscreteSDE

public class BMSDE
extends Object
implements DiscreteSDE
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).
"Fima C. Klebaner, "Section 3.1," Introduction to Stochastic Calculus with Applications, 2nd ed, Imperial College Press, 2006."
• ### Constructor Summary

Constructors
Constructor and Description
BMSDE()
Construct a univariate standard Brownian motion.
BMSDE(double mu, double sigma)
Construct a univariate Brownian motion.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double dXt(Ft ft)
This is the SDE specification of a stochastic process.
Ft getNewFt()
Get an empty filtration of the process.
• ### Methods inherited from class java.lang.Object

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

• #### BMSDE

public BMSDE(double mu,
double sigma)
Construct a univariate Brownian motion.
Parameters:
mu - μ, the drift
sigma - σ, the diffusion constant
• #### BMSDE

public BMSDE()
Construct a univariate standard Brownian motion.
• ### Method Detail

• #### dXt

public double dXt(Ft ft)
Description copied from interface: DiscreteSDE
This is the SDE specification of a stochastic process.
Specified by:
dXt in interface DiscreteSDE
Parameters:
ft - filtration
Returns:
the increment of the process in dt
• #### getNewFt

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