# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.random

## Class MultivariateBrownianRRG

• java.lang.Object
• com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.random.MultivariateBrownianRRG
• All Implemented Interfaces:
Seedable, MultivariateRandomRealizationGenerator

public class MultivariateBrownianRRG
extends Object
implements MultivariateRandomRealizationGenerator
This is the Random Walk construction of a multivariate Brownian motion.

For constant μ and σ, this method is exact in the sense that the joint distribution of the simulated values coincides with the joint distribution of the corresponding Brownian motion a the time grid points. Please note that this says nothing about what happens between two successive grid points.

For time-dependent μ and σ, this method in general introduce discretization error even at the time grid points, because the increments will no longer have exactly the correct mean and variance.

"P. Glasserman, "Section 3.1, pp. 81," Monte Carlo Methods in Financial Engineering, Springer, 2004."
• ### Constructor Summary

Constructors
Constructor and Description
MultivariateBrownianRRG(int d, int T)
Construct a random realization generator to produce multi-dimensional Brownian paths at evenly spaced time points [0, 1, ...].
MultivariateBrownianRRG(int d, TimeGrid timePoints)
Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
MultivariateBrownianRRG(int d, TimeGrid timePoints, Vector initial)
Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
• ### Method Summary

All Methods
Modifier and Type Method and Description
MultivariateRealization nextRealization()
Construct a realization of a multivariate stochastic process.
void seed(long... seeds)
Seed the random number/vector/scenario generator to produce repeatable experiments.
• ### Methods inherited from class java.lang.Object

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

• #### MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
TimeGrid timePoints,
Vector initial)
Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
Parameters:
d - the dimension of the Brownian motion
timePoints - specifying the time points in a grid
initial - the initial value of the process
• #### MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
TimeGrid timePoints)
Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
Parameters:
d - the dimension of the Brownian motion
timePoints - specifying the time points in a grid
• #### MultivariateBrownianRRG

public MultivariateBrownianRRG(int d,
int T)
Construct a random realization generator to produce multi-dimensional Brownian paths at evenly spaced time points [0, 1, ...].
Parameters:
d - the dimension of the Brownian motion
T - the number of time points
• ### Method Detail

• #### seed

public void seed(long... seeds)
Description copied from interface: Seedable
Seed the random number/vector/scenario generator to produce repeatable experiments.
Specified by:
seed in interface Seedable
Parameters:
seeds - the seeds
• #### nextRealization

public MultivariateRealization nextRealization()
Description copied from interface: MultivariateRandomRealizationGenerator
Construct a realization of a multivariate stochastic process.
Specified by:
nextRealization in interface MultivariateRandomRealizationGenerator
Returns:
a realization