This class represents a gamma process [167] (page 82) \(\{ S(t) = G(t; \mu, \nu) : t \geq0 \}\) with mean parameter. More...

Inheritance diagram for umontreal.ssj.stochprocess.GammaProcess:

Public Member Functions
	GammaProcess (double s0, double mu, double nu, RandomStream stream)
	Constructs a new GammaProcess with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).
	GammaProcess (double s0, double mu, double nu, GammaGen Ggen)
	Constructs a new GammaProcess with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).
double	nextObservation ()
	Generates and returns the next observation \(X(t_j)\) of the stochastic process.
double	nextObservation (double nextT)
	Generates and returns the next observation at time \(t_{j+1} = \mathtt{nextTime}\), 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 \(X(t_j)\).
double[]	generatePath ()
	Generates, returns and saves the path \(\{X(t_0), X(t_1), …, X(t_d)\}\).
double[]	generatePath (double[] uniform01)
	Generates, returns and saves the path \( \{X(t_0), X(t_1), …, X(t_d)\}\).
void	setParams (double s0, double mu, double nu)
	Sets the parameters \(S(t_0) = \mathtt{s0}\), \(\mu= \mathtt{mu}\) and \(\nu= \mathtt{nu}\) of the process.
double	getMu ()
	Returns the value of the parameter \(\mu\).
double	getNu ()
	Returns the value of the parameter \(\nu\).
void	setStream (RandomStream stream)
	Resets the umontreal.ssj.rng.RandomStream of the.
RandomStream	getStream ()
	Returns the umontreal.ssj.rng.RandomStream stream.
Public Member Functions inherited from umontreal.ssj.stochprocess.StochasticProcess
void	setObservationTimes (double[] T, int d)
	Sets the observation times of the process to a copy of T, with.
void	setObservationTimes (double delta, int d)
	Sets equidistant observation times at \(t_j = j\delta\), for.
double[]	getObservationTimes ()
	Returns a reference to the array that contains the observation times.
int	getNumObservationTimes ()
	Returns the number \(d\) of observation times, excluding the time \(t_0\).
double[]	generatePath (RandomStream stream)
	Same as generatePath(), but first resets the stream to stream.
double[]	getPath ()
	Returns a reference to the last generated sample path \(\{X(t_0), ... , X(t_d)\}\).
void	getSubpath (double[] subpath, int[] pathIndices)
	Returns in subpath the values of the process at a subset of the observation times, specified as the times \(t_j\) whose indices.
double	getObservation (int j)
	Returns \(X(t_j)\) from the current sample path.
void	resetStartProcess ()
	Resets the observation counter to its initial value \(j=0\), so that the current observation \(X(t_j)\) becomes \(X(t_0)\).
boolean	hasNextObservation ()
	Returns true if \(j<d\), where \(j\) is the number of observations of the current sample path generated since the last call to resetStartProcess.
int	getCurrentObservationIndex ()
	Returns the value of the index \(j\) corresponding to the time.
double	getCurrentObservation ()
	Returns the value of the last generated observation \(X(t_j)\).
double	getX0 ()
	Returns the initial value \(X(t_0)\) for this process.
void	setX0 (double s0)
	Sets the initial value \(X(t_0)\) for this process to s0, and reinitializes.
int[]	getArrayMappingCounterToIndex ()
	Returns a reference to an array that maps an integer \(k\) to \(i_k\), the index of the observation \(S(t_{i_k})\) corresponding to the.

Detailed Description

This class represents a gamma process [167] (page 82) \(\{ S(t) = G(t; \mu, \nu) : t \geq0 \}\) with mean parameter.

\(\mu\) and variance parameter \(\nu\). It is a continuous-time process with stationary, independent gamma increments such that for any \(\Delta t > 0\),

\[ S(t + \Delta t) = S(t) + X,\tag{GammaEqn} \]

where \(X\) is a random variate from the gamma distribution Gamma \((\mu^2\Delta t / \nu, \mu/ \nu)\).

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

Definition at line 48 of file GammaProcess.java.

Constructor & Destructor Documentation

◆ GammaProcess() [1/2]

umontreal.ssj.stochprocess.GammaProcess.GammaProcess	(	double	s0,
		double	mu,
		double	nu,
		RandomStream	stream )

Constructs a new GammaProcess with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).

The gamma variates \(X\) in ( GammaEqn ) are generated by inversion using stream.

Definition at line 108 of file GammaProcess.java.

◆ GammaProcess() [2/2]

umontreal.ssj.stochprocess.GammaProcess.GammaProcess	(	double	s0,
		double	mu,
		double	nu,
		GammaGen	Ggen )

Constructs a new GammaProcess with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).

The gamma variates \(X\) in ( GammaEqn ) are supplied by the gamma random variate generator Ggen. Note that the parameters of the

umontreal.ssj.randvar.GammaGen object Ggen are not important since the implementation forces the generator to use the correct parameters (as defined above).

Definition at line 126 of file GammaProcess.java.

Member Function Documentation

◆ generatePath() [1/2]

double[] umontreal.ssj.stochprocess.GammaProcess.generatePath ( )

Generates, returns and saves the path \(\{X(t_0), X(t_1), …, X(t_d)\}\).

The gamma variates \(X\) in ( GammaEqn ) are generated using the

umontreal.ssj.rng.RandomStream stream or the umontreal.ssj.rng.RandomStream included in the umontreal.ssj.randvar.GammaGen Ggen.

Reimplemented from umontreal.ssj.stochprocess.StochasticProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessBridge, umontreal.ssj.stochprocess.GammaProcessPCA, umontreal.ssj.stochprocess.GammaProcessPCABridge, umontreal.ssj.stochprocess.GammaProcessPCASymmetricalBridge, and umontreal.ssj.stochprocess.GammaProcessSymmetricalBridge.

Definition at line 179 of file GammaProcess.java.

◆ generatePath() [2/2]

double[] umontreal.ssj.stochprocess.GammaProcess.generatePath ( double[] uniform01 )

Generates, returns and saves the path \( \{X(t_0), X(t_1), …, X(t_d)\}\).

This method does not use the

umontreal.ssj.rng.RandomStream stream nor the umontreal.ssj.randvar.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 \(d\).

Reimplemented in umontreal.ssj.stochprocess.GammaProcessBridge, umontreal.ssj.stochprocess.GammaProcessPCA, umontreal.ssj.stochprocess.GammaProcessPCABridge, umontreal.ssj.stochprocess.GammaProcessPCASymmetricalBridge, and umontreal.ssj.stochprocess.GammaProcessSymmetricalBridge.

Definition at line 203 of file GammaProcess.java.

◆ getMu()

double umontreal.ssj.stochprocess.GammaProcess.getMu ( )

Returns the value of the parameter \(\mu\).

Definition at line 235 of file GammaProcess.java.

◆ getNu()

double umontreal.ssj.stochprocess.GammaProcess.getNu ( )

Returns the value of the parameter \(\nu\).

Definition at line 242 of file GammaProcess.java.

◆ getStream()

RandomStream umontreal.ssj.stochprocess.GammaProcess.getStream ( )

Returns the umontreal.ssj.rng.RandomStream stream.

Reimplemented from umontreal.ssj.stochprocess.StochasticProcess.

Definition at line 259 of file GammaProcess.java.

◆ nextObservation() [1/2]

double umontreal.ssj.stochprocess.GammaProcess.nextObservation ( )

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.

Reimplemented from umontreal.ssj.stochprocess.StochasticProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessBridge, umontreal.ssj.stochprocess.GammaProcessPCA, and umontreal.ssj.stochprocess.GammaProcessSymmetricalBridge.

Definition at line 134 of file GammaProcess.java.

◆ nextObservation() [2/2]

double umontreal.ssj.stochprocess.GammaProcess.nextObservation ( double nextT )

Generates and returns the next observation at time \(t_{j+1} = \mathtt{nextTime}\), 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 \(\geq t_j\).

Reimplemented in umontreal.ssj.stochprocess.GammaProcessBridge, umontreal.ssj.stochprocess.GammaProcessPCA, and umontreal.ssj.stochprocess.GammaProcessSymmetricalBridge.

Definition at line 154 of file GammaProcess.java.