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

Class RandomWalk

java.lang.Object

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

com.numericalmethod.suanshu.stats.stochasticprocess.univariate.brownian.RandomWalk

All Implemented Interfaces:

Construction, DiscretizedSDE, java.io.Serializable

public class RandomWalk
extends Brownian
implements Construction

This is the Random Walk construction of a univariate 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.", Serialized Form

Field Summary

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

mu, sigma

Constructor Summary

Constructors

Constructor and Description
RandomWalk(int T) Construct a univariate Brownian motion at even time points, [0, 1, ......, T].
RandomWalk(TimeGrid timePoints) Construct a univariate Brownian motion at time points specified.

Method Summary

Modifier and Type	Method and Description
RandomWalk.Realization	nextRealization(double x0) Construct a realization of the 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.univariate.brownian.Brownian

dXt, getNewFt

Methods inherited from class java.lang.Object

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

Constructor Detail

RandomWalk

public RandomWalk(TimeGrid timePoints)

Construct a univariate Brownian motion at time points specified.

Parameters:

timePoints - specifying the time points in a grid

RandomWalk

public RandomWalk(int T)

Construct a univariate Brownian motion at even time points, [0, 1, ......, T].

Parameters:

T - the length of the grid

Method Detail

nextRealization

public RandomWalk.Realization nextRealization(double x0)

Description copied from interface: Construction

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

Specified by:

nextRealization 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