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

java.lang.Object
  com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian.Brownian
      com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian.RandomWalk

All Implemented Interfaces:

Construction, DiscretizedSDE

public class RandomWalk
extends Brownian
implements Construction

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.

See Also:

"P. Glasserman. Monte Carlo Methods in Financial Engineering. Section 3.1. pp. 81. Springer. 2004."

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian.Brownian

d, mu, sigma

Constructor Summary

RandomWalk(int d, int T)
Construct a multi-dimensional Brownian motion at even time points, [0, 1, ......, T].

RandomWalk(int d, TimeGrid timePoints)
Construct a multi-dimensional Brownian motion at time points specified.

Method Summary

MultiVariateRealization	realization(Vector x0) Construct a realization of a stochastic process.
void	seed(long seed) Seed the construction process so that we may generate the same realizations.

Methods inherited from class com.numericalmethod.suanshu.stats.stochasticprocess.multivariate.brownian.Brownian

dXt, getNewFt, nB

Methods inherited from class java.lang.Object

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

Constructor Detail

RandomWalk

public RandomWalk(int d,
                  TimeGrid timePoints)

Construct a multi-dimensional Brownian motion at time points specified.

Parameters:

d - the dimension of the Brownian motion

timePoints - specifying the time points in a grid

RandomWalk

public RandomWalk(int d,
                  int T)

Construct a multi-dimensional Brownian motion at even time points, [0, 1, ......, T].

Parameters:

d - the dimension of the Brownian motion

T - the length of the grid

Method Detail

realization

public MultiVariateRealization realization(Vector x0)

Description copied from interface: Construction

Construct a realization of a stochastic process. The realization is a time series.

Specified by:

realization in interface Construction

Parameters:

x0 - the starting point of the trajectory

Returns:

a realization

seed

public void seed(long seed)

Description copied from interface: Construction

Seed the construction process so that we may generate the same realizations.

Specified by:

seed in interface Construction

Parameters:

seed - seeding the same seed gives arise to the same realization