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

Inheritance diagram for umontreal.ssj.stochprocess.MultivariateBrownianMotionPCABigSigma:

Public Member Functions
	MultivariateBrownianMotionPCABigSigma (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream)
	Constructs a new MultivariateBrownianMotionPCABigSigma with parameters \(\boldsymbol{\mu}= \mathtt{mu}\),.
	MultivariateBrownianMotionPCABigSigma (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen)
	Constructs a new MultivariateBrownianMotionPCABigSigma with parameters \(\boldsymbol{\mu}= \mathtt{mu}\),.
void	setParams (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ)
	Sets the dimension \(c = \mathtt{c}\), the initial value.
double[]	generatePath ()
	Generates, returns, and saves the sample path.
double[]	generatePath (double[] uniform01)
	Same as generatePath() but requires a vector of uniform random numbers which are used to generate the path.
Public Member Functions inherited from umontreal.ssj.stochprocess.MultivariateBrownianMotion
	MultivariateBrownianMotion (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream)
	Constructs a new MultivariateBrownianMotion with parameters.
	MultivariateBrownianMotion (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen)
	Constructs a new MultivariateBrownianMotion with parameters.
void	nextObservationVector (double[] obs)
	Generates and returns in obs the next observation.
double[]	nextObservationVector ()
	Generates and returns the next observation \(\mathbf{X}(t_j)\) of the multivariate stochastic process in a vector created automatically.
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 \(X(t_j)\).
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.
double[]	generatePath (RandomStream stream)
	Same as generatePath(), but first resets the stream to stream.
void	setParams (double x0[], double mu[], double sigma[])
	Sets the dimension \(c = \mathtt{c}\), the initial value.
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.
double[]	getMu ()
	Returns the vector mu.
Public Member Functions inherited from umontreal.ssj.stochprocess.MultivariateStochasticProcess
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.
void	setObservationTimes (double[] t, int d)
	Sets the observation times of the process to a copy of t, with.
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.
void	getCurrentObservation (double[] obs)
	Returns the value of the last generated observation.
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 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[]	getPath ()
	Returns a reference to the last generated sample path \(\{X(t_0), ... , X(t_d)\}\).
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.
double	nextObservation ()
	Generates and returns the next observation \(X(t_j)\) of the stochastic process.
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

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.

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Definition at line 48 of file MultivariateBrownianMotionPCABigSigma.java.

Constructor & Destructor Documentation

◆ MultivariateBrownianMotionPCABigSigma() [1/2]

umontreal.ssj.stochprocess.MultivariateBrownianMotionPCABigSigma.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.

Definition at line 68 of file MultivariateBrownianMotionPCABigSigma.java.

◆ MultivariateBrownianMotionPCABigSigma() [2/2]

umontreal.ssj.stochprocess.MultivariateBrownianMotionPCABigSigma.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.

Definition at line 84 of file MultivariateBrownianMotionPCABigSigma.java.

Member Function Documentation

◆ generatePath() [1/2]

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

Generates, returns, and saves the sample path.

\(\{\mathbf{X}(t_0), \mathbf{X}(t_1), …, \mathbf{X}(t_d)\}\), which can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type. If path[] denotes the returned array, then path[cj + i-1] contains \(X_i(t_j)\) for \(j=0,…,d\) and \(i=1,…,c\).

Reimplemented from umontreal.ssj.stochprocess.MultivariateBrownianMotion.

Definition at line 131 of file MultivariateBrownianMotionPCABigSigma.java.

◆ generatePath() [2/2]

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

Same as generatePath() but requires a vector of uniform random numbers which are used to generate the path.

Reimplemented from umontreal.ssj.stochprocess.MultivariateBrownianMotion.

Definition at line 155 of file MultivariateBrownianMotionPCABigSigma.java.

◆ setParams()

void umontreal.ssj.stochprocess.MultivariateBrownianMotionPCABigSigma.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. The vectors x0, mu ans sigma must be of size c as well as the matrix corrZ must be of size c x c. Warning: This method will recompute some quantities stored internally, which may be slow if called too frequently.

Reimplemented from umontreal.ssj.stochprocess.MultivariateBrownianMotion.

Definition at line 91 of file MultivariateBrownianMotionPCABigSigma.java.

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

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

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ MultivariateBrownianMotionPCABigSigma() [1/2]

◆ MultivariateBrownianMotionPCABigSigma() [2/2]

Member Function Documentation

◆ generatePath() [1/2]

◆ generatePath() [2/2]

◆ setParams()