SSJ  3.3.1
Stochastic Simulation in Java
Public Member Functions | Protected Member Functions | Protected Attributes | Package Attributes | List of all members
MultivariateBrownianMotionPCABigSigma Class Reference

A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled entirely using the principal component decomposition (PCA). More...

Inheritance diagram for MultivariateBrownianMotionPCABigSigma:
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Collaboration diagram for MultivariateBrownianMotionPCABigSigma:
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Public Member Functions

 MultivariateBrownianMotionPCABigSigma (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream)
 Constructs a new MultivariateBrownianMotionPCABigSigma 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...
 
 MultivariateBrownianMotionPCABigSigma (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen)
 Constructs a new MultivariateBrownianMotionPCABigSigma 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)
 
- 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 BigSigma)
 
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 BigSigma
 
DoubleMatrix2D decompPCABigSigma
 
DoubleMatrix2D C
 
DoubleMatrix2D A
 
double [] z
 
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

double [] zz
 
- 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).

In this class, a matrix which equals the Kronecker products of two matrices C and \(\Sigma\) must be computed. C is the usual one dimensional Brownian motion covariance matrix and \(\Sigma\) is the matrix that defined the covariance between the one dimensionnal Brownian motion. This Kronecker products is time and memory consuming as it might creates an enormous matrix, matrix that is called BigSigma here. The class MultivariateBrownianMotionPCA provides faster results.

Constructor & Destructor Documentation

◆ MultivariateBrownianMotionPCABigSigma() [1/2]

MultivariateBrownianMotionPCABigSigma ( int  c,
double []  x0,
double []  mu,
double []  sigma,
double  corrZ[][],
RandomStream  stream 
)

Constructs a new MultivariateBrownianMotionPCABigSigma 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.

◆ MultivariateBrownianMotionPCABigSigma() [2/2]

MultivariateBrownianMotionPCABigSigma ( int  c,
double []  x0,
double []  mu,
double []  sigma,
double  corrZ[][],
NormalGen  gen 
)

Constructs a new MultivariateBrownianMotionPCABigSigma 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: