A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled entirely using the principal component decomposition (PCA), as explained in [69] , page 92. More...
Inheritance diagram for MultivariateBrownianMotionPCA:
Collaboration diagram for MultivariateBrownianMotionPCA:
Public Member Functions | |
| MultivariateBrownianMotionPCA (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream) | |
Constructs a new MultivariateBrownianMotionPCA with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\). More... | |
| MultivariateBrownianMotionPCA (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen) | |
Constructs a new MultivariateBrownianMotionPCA with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\). More... | |
| void | setParams (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ) |
| double [] | generatePath () |
| double [] | generatePath (double[] uniform01) |
| Sets the parameters. | |
 Public Member Functions inherited from MultivariateBrownianMotion | |
| MultivariateBrownianMotion (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream) | |
Constructs a new MultivariateBrownianMotion with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\). More... | |
| MultivariateBrownianMotion (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen) | |
Constructs a new MultivariateBrownianMotion with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\). More... | |
| void | nextObservationVector (double[] obs) |
Generates and returns in obs the next observation \(\mathbf{X}(t_j)\) of the multivariate stochastic process. More... | |
| double [] | nextObservationVector () |
| Generates and returns the next observation \(\mathbf{X}(t_j)\) of the multivariate stochastic process in a vector created automatically. More... | |
| double [] | nextObservationVector (double nextTime, double[] obs) |
Generates and returns the vector of next observations, 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 [] | nextObservationVector (double x[], double dt) |
Generates an observation (vector) of the process in dt time units, assuming that the process has (vector) value \(x\) at the current time. More... | |
| double [] | generatePath () |
| double [] | generatePath (double[] uniform01) |
Same as generatePath() but requires a vector of uniform random numbers which are used to generate the path. | |
| double [] | generatePath (RandomStream stream) |
| void | setParams (int c, double x0[], double mu[], double sigma[], double corrZ[][]) |
Sets the dimension \(c = \mathtt{c}\), the initial value \(\mathbf{X}(t_0) = \mathtt{x0}\), the average \(\mu= \mathtt{mu}\), the volatility \(\sigma= \mathtt{sigma}\) and the correlation matrix to corrZ. More... | |
| void | setParams (double x0[], double mu[], double sigma[]) |
| Sets the dimension \(c = \mathtt{c}\), the initial value \(\mathbf{X}(t_0) = \mathtt{x0}\), the average \(\mu= \mathtt{mu}\), the volatility \(\sigma= \mathtt{sigma}\). More... | |
| void | setStream (RandomStream stream) |
Resets the random stream of the normal generator to stream. | |
| RandomStream | getStream () |
| Returns the random stream of the normal generator. | |
| NormalGen | getGen () |
| Returns the normal random variate generator used. More... | |
| double [] | getMu () |
Returns the vector mu. | |
| Public Member Functions inherited from MultivariateStochasticProcess | |
| abstract double [] | generatePath () |
| Generates, returns, and saves the sample path. 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... | |
| void | setObservationTimes (double[] t, int d) |
Sets the observation times of the process to a copy of t, with. More... | |
| void | getObservation (int j, double[] obs) |
Returns \(\mathbf{X}(t_j)\) in the \(c\)-dimensional vector obs. | |
| double | getObservation (int j, int i) |
| Returns \(X_i(t_j)\) from the current sample path. | |
| abstract void | nextObservationVector (double[] obs) |
Generates and returns in obs the next observation. More... | |
| void | getCurrentObservation (double[] obs) |
| Returns the value of the last generated observation. More... | |
| double [] | getX0 (double[] x0) |
Returns in x0 the initial value \(\mathbf{X}(t_0)\) for this process. | |
| int | getDimension () |
| Returns the dimension of \(\mathbf{X}\). | |
| 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... | |
Protected Member Functions | |
| DoubleMatrix2D | decompPCA (DoubleMatrix2D Sigma, double[] eigenValues) |
| void | init () |
| Protected Member Functions inherited from MultivariateBrownianMotion | |
| void | init () |
| void | initCovZCholDecomp () |
| void | initCovZ () |
| Protected Member Functions inherited from MultivariateStochasticProcess | |
| void | init () |
| void | createPath () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
Protected Attributes | |
| DoubleMatrix2D | C |
| DoubleMatrix2D | BC |
| DoubleMatrix2D | PcovZ |
| double [] | z |
| int [] | eigenIndex |
| boolean | decompPCA |
| Protected Attributes inherited from MultivariateBrownianMotion | |
| NormalGen | gen |
| double [] | mu |
| double [] | sigma |
| double [][] | corrZ |
| DoubleMatrix2D | covZ |
| DoubleMatrix2D | covZCholDecomp |
| CholeskyDecomposition | decomp |
| boolean | covZiSCholDecomp |
| double [] | dt |
| Protected Attributes inherited from MultivariateStochasticProcess | |
| double [] | x0 |
| int | c = 1 |
| 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 |
Package Attributes | |
| DoubleMatrix2D | sortedBC |
| DoubleMatrix2D | copyBC |
| DoubleMatrix2D | PC |
| double [] | zz |
| double [] | zzz |
| Package Attributes inherited from MultivariateBrownianMotion | |
| double [] | sqrdt |
Detailed Description
A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled entirely using the principal component decomposition (PCA), as explained in [69] , page 92.
We construct the same matrix \(\boldsymbol{\Sigma}\) as in MultivariateBrownianMotion and decompose it as \(\boldsymbol{\Sigma}= B B^{\mathsf{t}}\) via PCA. We also compute the matrix \(\mathbf{C}\) whose element \((i,j)\) is \(\mathrm{Cov}[B(t_{i+1}),B(t_{j+1})] = \min(t_{i+1},t_{j+1})\) and its PCA decomposition \(\mathbf{C}= \mathbf{A}\mathbf{A}^{\mathsf{t}}\), as in class BrownianMotionPCA.
Constructor & Destructor Documentation
◆ MultivariateBrownianMotionPCA() [1/2]
| MultivariateBrownianMotionPCA | ( | int | c, |
| double [] | x0, | ||
| double [] | mu, | ||
| double [] | sigma, | ||
| double | corrZ[][], | ||
| RandomStream | stream | ||
| ) |
Constructs a new MultivariateBrownianMotionPCA with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\).
The normal variates \(Z_j\) in are generated by inversion using the umontreal.ssj.rng.RandomStream stream.
◆ MultivariateBrownianMotionPCA() [2/2]
| MultivariateBrownianMotionPCA | ( | int | c, |
| double [] | x0, | ||
| double [] | mu, | ||
| double [] | sigma, | ||
| double | corrZ[][], | ||
| NormalGen | gen | ||
| ) |
Constructs a new MultivariateBrownianMotionPCA with parameters \(\boldsymbol{\mu}= \mathtt{mu}\), \(\boldsymbol{\sigma}= \mathtt{sigma}\), correlation matrix \(\mathbf{R}_z = \mathtt{corrZ}\), and initial value \(\mathbf{X}(t_0) = \mathtt{x0}\).
The normal variates \(Z_j\) in are generated by gen.
The documentation for this class was generated from the following file:
- MultivariateBrownianMotionPCA.java
