MultivariateBrownianMotionBridge Class Reference

A multivariate Brownian motion process $\{\mathbf{X}(t) : t \geq0 \}$ sampled via bridge sampling. More...

Inheritance diagram for MultivariateBrownianMotionBridge:

Collaboration diagram for MultivariateBrownianMotionBridge:

Public Member Functions
	MultivariateBrownianMotionBridge (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, RandomStream stream)
	Constructs a new MultivariateBrownianMotionBridge with parameters $\boldsymbol{\mu}=$mu, $\boldsymbol{\sigma}=$sigma, correlation matrix $\mathbf{R}_z =$corrZ, and initial value $\mathbf{X}(t_0) =$x0. More...
	MultivariateBrownianMotionBridge (int c, double[] x0, double[] mu, double[] sigma, double[][] corrZ, NormalGen gen)
	Constructs a new MultivariateBrownianMotionBridge with parameters $\boldsymbol{\mu}=$mu, $\boldsymbol{\sigma}=$sigma, correlation matrix $\mathbf{R}_z =$corrZ, and initial value $\mathbf{X}(t_0) =$x0. More...
double []	generatePath ()
void	resetStartProcess ()
double []	nextObservationVector ()
void	nextObservationVector (double[] obs)
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
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
double []	z
int	bridgeCounter = -1
double []	wMuDt
int []	wIndexList
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 []	covZCholDecompz
double []	wSqrtDt
int []	ptIndex
Package Attributes inherited from MultivariateBrownianMotion
double []	sqrdt

Detailed Description

A multivariate Brownian motion process $\{\mathbf{X}(t) : t \geq0 \}$ sampled via bridge sampling.

We use a Cholesky decomposition of the relevant covariance matrix to generate the next $c$-dimensional vector at each step of the bridge sampling algorithm. For this, we construct the same matrix $\boldsymbol{\Sigma}$ as in MultivariateBrownianMotion and we compute its Cholesky decomposition $\boldsymbol{\Sigma}= B B^{\mathsf{t}}$.

Constructor & Destructor Documentation

MultivariateBrownianMotionBridge() [1/2]

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

Constructs a new MultivariateBrownianMotionBridge with parameters $\boldsymbol{\mu}=$mu, $\boldsymbol{\sigma}=$sigma, correlation matrix $\mathbf{R}_z =$corrZ, and initial value $\mathbf{X}(t_0) =$x0.

The normal variates $Z_j$ in are generated by inversion using the umontreal.ssj.rng.RandomStream stream.

MultivariateBrownianMotionBridge() [2/2]

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

Constructs a new MultivariateBrownianMotionBridge with parameters $\boldsymbol{\mu}=$mu, $\boldsymbol{\sigma}=$sigma, correlation matrix $\mathbf{R}_z =$corrZ, and initial value $\mathbf{X}(t_0) =$x0.

The normal variates $Z_j$ in are generated by gen.

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

• MultivariateBrownianMotionBridge.java