umontreal.iro.lecuyer.stochprocess

Class GammaProcess

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.GammaProcess

Direct Known Subclasses:

GammaProcessBridge, GammaProcessPCA

public class GammaProcess
extends StochasticProcess

This class represents a gamma process {S(t) = G(t;μ, ν) : t >= 0} with mean parameter μ and variance parameter ν. It is a continuous-time process with stationary, independent gamma increments such that for any Δt > 0,

S(t + Δt) = S(t) + X,

where X is a random variate from the gamma distribution Gamma (μ²Δt/ν, μ/ν).

In this class, the gamma process is sampled sequentially using equation.

Field Summary

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

path

Constructor Summary

Constructors

Constructor and Description
GammaProcess(double s0, double mu, double nu, GammaGen Ggen) Constructs a new GammaProcess with parameters μ = mu, ν = nu and initial value S(t0) = s0.
GammaProcess(double s0, double mu, double nu, RandomStream stream) Constructs a new GammaProcess with parameters μ = mu, ν = nu and initial value S(t0) = s0.

Method Summary

Methods

Modifier and Type	Method and Description
double[]	generatePath() Generates, returns and saves the path {X(t0), X(t1),…, X(td)}.
double[]	generatePath(double[] uniform01) Generates, returns and saves the path {X(t0), X(t1),…, X(td)}.
double	getMu() Returns the value of the parameter μ.
double	getNu() Returns the value of the parameter ν.
RandomStream	getStream() Returns the RandomStream stream.
double	nextObservation() Generates and returns the next observation X(tj) of the stochastic process.
double	nextObservation(double nextT) Generates and returns the next observation at time tj+1 = nextTime, using the previous observation time tj defined earlier (either by this method or by setObservationTimes), as well as the value of the previous observation X(tj).
void	setParams(double s0, double mu, double nu) Sets the parameters S(t0) = s0, μ = mu and ν = nu of the process.
void	setStream(RandomStream stream) Resets the RandomStream of the GammaGen to stream.

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

generatePath, 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

GammaProcess

public GammaProcess(double s0,
            double mu,
            double nu,
            RandomStream stream)

Constructs a new GammaProcess with parameters μ = mu, ν = nu and initial value S(t₀) = s0. The gamma variates X in are generated by inversion using stream.

GammaProcess

public GammaProcess(double s0,
            double mu,
            double nu,
            GammaGen Ggen)

Constructs a new GammaProcess with parameters μ = mu, ν = nu and initial value S(t₀) = s0. The gamma variates X in are supplied by the gamma random variate generator Ggen. Note that the parameters of the GammaGen object Ggen are not important since the implementation forces the generator to use the correct parameters (as defined above).

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 StochasticProcess

nextObservation

public double nextObservation(double nextT)

Generates and returns the next observation at time t_j+1 = nextTime, using the previous observation time t_j defined earlier (either by this method or by setObservationTimes), as well as the value of the previous observation X(t_j). Warning: This method will reset the observations time t_j+1 for this process to nextT. The user must make sure that the t_j+1 supplied is >= t_j.

generatePath

public double[] generatePath()

Generates, returns and saves the path {X(t₀), X(t₁),…, X(t_d)}. The gamma variates X in are generated using the RandomStream stream or the RandomStream included in the GammaGen Ggen.

Specified by:

generatePath in class StochasticProcess

generatePath

public double[] generatePath(double[] uniform01)

Generates, returns and saves the path {X(t₀), X(t₁),…, X(t_d)}. This method does not use the RandomStream stream nor the GammaGen Ggen. It uses the vector of uniform random numbers U(0, 1) provided by the user and generates the path by inversion. The vector uniform01 must be of dimension d.

setParams

public void setParams(double s0,
             double mu,
             double nu)

Sets the parameters S(t₀) = s0, μ = mu and ν = nu of the process. Warning: This method will recompute some quantities stored internally, which may be slow if called repeatedly.

getMu

public double getMu()

Returns the value of the parameter μ.

getNu

public double getNu()

Returns the value of the parameter ν.

setStream

public void setStream(RandomStream stream)

Resets the RandomStream of the GammaGen to stream.

Specified by:

setStream in class StochasticProcess

getStream

public RandomStream getStream()

Returns the RandomStream stream.

Specified by:

getStream in class StochasticProcess