Represents a gamma process sampled using the principal component analysis (PCA). More...

Inheritance diagram for umontreal.ssj.stochprocess.GammaProcessPCA:

Public Member Functions
	GammaProcessPCA (double s0, double mu, double nu, RandomStream stream)
	Constructs a new GammaProcessPCA with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).
	GammaProcessPCA (double s0, double mu, double nu, GammaGen Ggen)
	Constructs a new GammaProcessPCA with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\).
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 \( \{X(t_0), X(t_1), …, X(t_d)\}\).
double	nextObservation ()
	This method is not implemented in this class since the path cannot be generated sequentially.
double	nextObservation (double nextT)
	This method is not implemented in this class since the path cannot be generated sequentially.
BrownianMotionPCA	getBMPCA ()
	Returns the BrownianMotionPCA that is included in the.
void	setObservationTimes (double[] t, int d)
	Sets the observation times of the GammaProcessPCA and the.
void	setParams (double s0, double mu, double nu)
	Sets the parameters s0, \(\mu\) and \(\nu\) to new values, and sets the variance parameters of the BrownianMotionPCA to \(\nu\).
void	setStream (RandomStream stream)
	Resets the umontreal.ssj.rng.RandomStream of the gamma generator and the umontreal.ssj.rng.RandomStream of the inner.
Public Member Functions inherited from 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 \(S(t_0) = \mathtt{s0}\).
	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	getMu ()
	Returns the value of the parameter \(\mu\).
double	getNu ()
	Returns the value of the parameter \(\nu\).
RandomStream	getStream ()
	Returns the umontreal.ssj.rng.RandomStream stream.
Public Member Functions inherited from umontreal.ssj.stochprocess.StochasticProcess
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

Represents a gamma process sampled using the principal component analysis (PCA).

To simulate the gamma process at times \(t_0 < t_1 < \cdots< t_d\) by PCA sampling, a Brownian motion \(\{ W(t), t \geq0 \}\) with mean \(0\) and variance parameter \(\nu\) is first generated at times \(t_0 < t_1 < \cdots< t_d\) by PCA sampling (see class BrownianMotionPCA ). The independent increments \(W(t_j) - W(t_{j-1})\) of this process are then transformed into independent \(U(0, 1)\) random variates \(V_j\) via

\[ V_j = \Phi\left(\sqrt{\tau_j-\tau_{j-1}} [W(\tau_j)-W(\tau_{j-1})]\right), \quad j=1,…,s \]

Finally, the increments of the Gamma process are computed as \( Y(t_j) - Y(t_{j-1}) = G^{-1}(V_j)\), where \(G\) is the gamma distribution function.

Definition at line 48 of file GammaProcessPCA.java.

Constructor & Destructor Documentation

◆ GammaProcessPCA() [1/2]

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

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

The random variables are created using stream. Note that the same umontreal.ssj.rng.RandomStream is used for the GammaProcessPCA and for the BrownianMotionPCA included in this class. Both the GammaProcessPCA and the

BrownianMotionPCA are generated by inversion.

Definition at line 62 of file GammaProcessPCA.java.

◆ GammaProcessPCA() [2/2]

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

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

All the random variables, i.e. the gamma ones and the normal ones, are created using the

umontreal.ssj.rng.RandomStream included in the umontreal.ssj.randvar.GammaGen Ggen. Note that the parameters of the umontreal.ssj.randvar.GammaGen object are not important since the implementation forces the generator to use the correct parameters (as defined above).

Definition at line 79 of file GammaProcessPCA.java.

Member Function Documentation

◆ generatePath() [1/2]

double[] umontreal.ssj.stochprocess.GammaProcessPCA.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.GammaProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessPCABridge, and umontreal.ssj.stochprocess.GammaProcessPCASymmetricalBridge.

Definition at line 84 of file GammaProcessPCA.java.

◆ generatePath() [2/2]

double[] umontreal.ssj.stochprocess.GammaProcessPCA.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 from umontreal.ssj.stochprocess.GammaProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessPCABridge, and umontreal.ssj.stochprocess.GammaProcessPCASymmetricalBridge.

Definition at line 103 of file GammaProcessPCA.java.

◆ getBMPCA()

BrownianMotionPCA umontreal.ssj.stochprocess.GammaProcessPCA.getBMPCA ( )

Returns the BrownianMotionPCA that is included in the.

GammaProcessPCA object.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessPCABridge.

Definition at line 143 of file GammaProcessPCA.java.

◆ nextObservation() [1/2]

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

This method is not implemented in this class since the path cannot be generated sequentially.

Reimplemented from umontreal.ssj.stochprocess.GammaProcess.

Definition at line 126 of file GammaProcessPCA.java.

◆ nextObservation() [2/2]

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

This method is not implemented in this class since the path cannot be generated sequentially.

Reimplemented from umontreal.ssj.stochprocess.GammaProcess.

Definition at line 134 of file GammaProcessPCA.java.

◆ setObservationTimes()

void umontreal.ssj.stochprocess.GammaProcessPCA.setObservationTimes	(	double[]	t,
		int	d )

Sets the observation times of the GammaProcessPCA and the.

BrownianMotionPCA.

Reimplemented from umontreal.ssj.stochprocess.StochasticProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessPCABridge.

Definition at line 152 of file GammaProcessPCA.java.

◆ setParams()

void umontreal.ssj.stochprocess.GammaProcessPCA.setParams	(	double	s0,
		double	mu,
		double	nu )

Sets the parameters s0, \(\mu\) and \(\nu\) to new values, and sets the variance parameters of the BrownianMotionPCA to \(\nu\).

Reimplemented from umontreal.ssj.stochprocess.GammaProcess.

Reimplemented in umontreal.ssj.stochprocess.GammaProcessPCABridge.

Definition at line 161 of file GammaProcessPCA.java.

◆ setStream()

void umontreal.ssj.stochprocess.GammaProcessPCA.setStream ( RandomStream stream )

Resets the umontreal.ssj.rng.RandomStream of the gamma generator and the umontreal.ssj.rng.RandomStream of the inner.

BrownianMotionPCA to stream.

Reimplemented from umontreal.ssj.stochprocess.GammaProcess.

Definition at line 172 of file GammaProcessPCA.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/stochprocess/GammaProcessPCA.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ GammaProcessPCA() [1/2]

◆ GammaProcessPCA() [2/2]

Member Function Documentation

◆ generatePath() [1/2]

◆ generatePath() [2/2]

◆ getBMPCA()

◆ nextObservation() [1/2]

◆ nextObservation() [2/2]

◆ setObservationTimes()

◆ setParams()

◆ setStream()