Represents a gamma process sampled using the principal component analysis (PCA). More...
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 \(S(t_0) = \mathtt{s0}\). More... | |
| GammaProcessPCA (double s0, double mu, double nu, GammaGen Ggen) | |
Constructs a new GammaProcessPCA with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\). More... | |
| double [] | generatePath () |
| double [] | generatePath (double[] uniform01) |
| 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 GammaProcessPCA object. | |
| void | setObservationTimes (double[] t, int d) |
| Sets the observation times of the GammaProcessPCA and the BrownianMotionPCA. | |
| 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 BrownianMotionPCA to stream. | |
 Public Member Functions inherited from 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 \(S(t_0) = \mathtt{s0}\). More... | |
| GammaProcess (double s0, double mu, double nu, GammaGen Ggen) | |
Constructs a new GammaProcess with parameters \(\mu= \mathtt{mu}\), \(\nu= \mathtt{nu}\) and initial value \(S(t_0) = \mathtt{s0}\). More... | |
| double | nextObservation () |
| 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 \(X(t_j)\). More... | |
| double [] | generatePath () |
| Generates, returns and saves the path \(\{X(t_0), X(t_1), …, X(t_d)\}\). More... | |
| double [] | generatePath (double[] uniform01) |
| Generates, returns and saves the path \( \{X(t_0), X(t_1), …, X(t_d)\}\). More... | |
| 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. More... | |
| 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 umontreal.ssj.randvar.GammaGen to stream. | |
| RandomStream | getStream () |
Returns the umontreal.ssj.rng.RandomStream stream. | |
| Public Member Functions inherited from StochasticProcess | |
| void | setObservationTimes (double[] T, int d) |
Sets the observation times of the process to a copy of T, with. More... | |
| void | setObservationTimes (double delta, int d) |
| Sets equidistant observation times at \(t_j = j\delta\), for. More... | |
| double [] | getObservationTimes () |
| Returns a reference to the array that contains the observation times. More... | |
| int | getNumObservationTimes () |
| Returns the number \(d\) of observation times, excluding the time \(t_0\). | |
| abstract double [] | generatePath () |
| Generates, returns, and saves the sample path \(\{X(t_0), X(t_1), \dots, X(t_d)\}\). More... | |
| 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 \(\{X(t_0), ... , X(t_d)\}\). More... | |
| 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. More... | |
| double | getObservation (int j) |
| Returns \(X(t_j)\) from the current sample path. More... | |
| void | resetStartProcess () |
| Resets the observation counter to its initial value \(j=0\), so that the current observation \(X(t_j)\) becomes \(X(t_0)\). More... | |
| 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. More... | |
| double | nextObservation () |
| Generates and returns the next observation \(X(t_j)\) of the stochastic process. More... | |
| int | getCurrentObservationIndex () |
| Returns the value of the index \(j\) corresponding to the time. More... | |
| 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. | |
| abstract void | setStream (RandomStream stream) |
Resets the random stream of the underlying generator to stream. | |
| abstract RandomStream | getStream () |
| Returns the random stream of the underlying generator. | |
| 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 \(k\)-th observation to be generated for a sample path of this process. More... | |
Package Attributes | |
| double [] | arrayTime |
| BrownianMotionPCA | BMPCA |
| Package Attributes inherited from GammaProcess | |
| double | nu |
| double | mu2OverNu |
Additional Inherited Members | |
| Protected Member Functions inherited from GammaProcess | |
| void | setLarger (double[] path, int left, int mid, int right) |
| double | setLarger (double[] path, int left, int right) |
| double | setLarger (double v) |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
| Protected Attributes inherited from GammaProcess | |
| boolean | usesAnti = false |
| RandomStream | stream |
| GammaGen | Ggen |
| double | mu |
| double | muOverNu |
| double [] | mu2dtOverNu |
| Protected Attributes inherited from StochasticProcess | |
| boolean | observationTimesSet = false |
| double | x0 = 0.0 |
| int | d = -1 |
| int | observationIndex = 0 |
| int | observationCounter = 0 |
| double [] | t |
| double [] | path |
| int [] | observationIndexFromCounter |
| Static Protected Attributes inherited from GammaProcess | |
| static final double | EPS = 1.0e-15 |
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.
Constructor & Destructor Documentation
◆ GammaProcessPCA() [1/2]
| 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.
◆ GammaProcessPCA() [2/2]
| 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).
The documentation for this class was generated from the following file:
- GammaProcessPCA.java
