umontreal.iro.lecuyer.stochprocess

Class BrownianMotionPCA

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.BrownianMotion

umontreal.iro.lecuyer.stochprocess.BrownianMotionPCA

public class BrownianMotionPCA
extends BrownianMotion

A Brownian motion process {X(t) : t >= 0} sampled using the principal component decomposition (PCA).

Constructor Summary

Constructors

Constructor and Description
BrownianMotionPCA(double x0, double mu, double sigma, NormalGen gen) Constructs a new BrownianMotionBridge with parameters μ = mu, σ = sigma and initial value X(t0) = x0.
BrownianMotionPCA(double x0, double mu, double sigma, RandomStream stream) Constructs a new BrownianMotionBridge with parameters μ = mu, σ = sigma and initial value X(t0) = x0.

Method Summary

Modifier and Type	Method and Description
double[][]	decompPCA(double[][] sigma)
double[]	generatePath() Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}.
double[]	generatePath(double[] uniform01) Same as generatePath(), but a vector of uniform random numbers must be provided to the method.
double[]	getSortedEigenvalues() Returns the sorted eigenvalues obtained in the PCA decomposition.
double	nextObservation() Generates and returns the next observation X(tj) of the stochastic process.
void	setParams(double x0, double mu, double sigma) Resets the parameters X(t0) = x0, μ = mu and σ = sigma of the process.

Methods inherited from class umontreal.iro.lecuyer.stochprocess.BrownianMotion

generatePath, getGen, getMu, getSigma, getStream, nextObservation, nextObservation, setStream

Methods inherited from class umontreal.iro.lecuyer.stochprocess.StochasticProcess

getArrayMappingCounterToIndex, getCurrentObservation, getCurrentObservationIndex, getNbObservationTimes, getObservation, getObservationTimes, getPath, getSubpath, getX0, hasNextObservation, resetStartProcess, setObservationTimes, setObservationTimes, setX0

Methods inherited from class java.lang.Object

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

Constructor Detail

BrownianMotionPCA

public BrownianMotionPCA(double x0,
                         double mu,
                         double sigma,
                         RandomStream stream)

Constructs a new BrownianMotionBridge with parameters μ = mu, σ = sigma and initial value X(t₀) = x0. The normal variates will be generated by inversion using stream.

BrownianMotionPCA

public BrownianMotionPCA(double x0,
                         double mu,
                         double sigma,
                         NormalGen gen)

Constructs a new BrownianMotionBridge with parameters μ = mu, σ = sigma and initial value X(t₀) = x0. The normal variates will be generated by gen.

Method Detail

nextObservation

public double nextObservation()

Description copied from class: StochasticProcess

Generates and returns the next observation X(t_j) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time t_j-1, the next observation returned will be for time t_j. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the t_j's is then specified by the subclass. All the processes generated using principal components analysis (PCA) do not have this method.

Overrides:

nextObservation in class BrownianMotion

setParams

public void setParams(double x0,
                      double mu,
                      double sigma)

Description copied from class: BrownianMotion

Resets the parameters X(t₀) = x0, μ = mu and σ = sigma of the process. Warning: This method will recompute some quantities stored internally, which may be slow if called too frequently.

Overrides:

setParams in class BrownianMotion

generatePath

public double[] generatePath()

Description copied from class: StochasticProcess

Generates, returns, and saves the sample path {X(t₀), X(t₁),…, X(t_d)}. It can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type.

Overrides:

generatePath in class BrownianMotion

generatePath

public double[] generatePath(double[] uniform01)

Description copied from class: BrownianMotion

Same as generatePath(), but a vector of uniform random numbers must be provided to the method. These uniform random numbers are used to generate the path.

Overrides:

generatePath in class BrownianMotion

decompPCA

public double[][] decompPCA(double[][] sigma)

getSortedEigenvalues

public double[] getSortedEigenvalues()

Returns the sorted eigenvalues obtained in the PCA decomposition.