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

This class represents a multivariate Brownian motion process \(\{\mathbf{X}(t) = (X_1(t),…, X_c(t)),  t \geq0 \}\), sampled at times \(0 = t_0 < t_1 < \cdots< t_d\). More...

Inheritance diagram for MultivariateBrownianMotion:
[legend]
Collaboration diagram for MultivariateBrownianMotion:
[legend]

Public Member Functions

 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 ()
 
void initCovZCholDecomp ()
 
void initCovZ ()
 
- Protected Member Functions inherited from MultivariateStochasticProcess
void init ()
 
void createPath ()
 
- Protected Member Functions inherited from StochasticProcess
void init ()
 

Protected Attributes

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 [] sqrdt
 

Detailed Description

This class represents a multivariate Brownian motion process \(\{\mathbf{X}(t) = (X_1(t),…, X_c(t)),  t \geq0 \}\), sampled at times \(0 = t_0 < t_1 < \cdots< t_d\).

Each vector coordinate is a univariate Brownian motion \(\{X_i(t),  t \geq0 \}\), with drift and volatility parameters \(\mu_i\) and \(\sigma_i\), so it can be written as

\[ X_i(t_j) - X_i(t_{j-1}) = (t_j - t_{j-1})\mu_i + \sqrt{t_j - t_{j-1}} \sigma_i Z_{j,i} \tag{Brownian-motion-sequential-multi} \]

where \(X_i(0)=0\), each \(Z_{j,i} \sim N(0,1)\), and each \(\mathbf{Z}_j = (Z_{j,1},…,Z_{j,c})\) has correlation matrix \(\mathbf{R}_z\). We write \(\boldsymbol{\mu}= (\mu_1,…,\mu_c)^{\mathsf{t}}\), \(\boldsymbol{\sigma}= (\sigma_1,…,\sigma_c)^{\mathsf{t}}\), and \(\boldsymbol{\Sigma}\) for the covariance matrix of \(\mathbf{X}(1)-\mathbf{X}(0)\), which equals \(\boldsymbol{\Sigma}= \boldsymbol{\sigma}\mathbf{R}_z\boldsymbol{\sigma}^{\mathsf{t}}\) (so the element \((k,l)\) or \(\boldsymbol{\Sigma}\) is the element \((k,l)\) of \(\mathbf{R}_z\) multiplied by \(\sigma_k\sigma_l\)). The trajectories are sampled by the sequential (or random walk) method.

Constructor & Destructor Documentation

◆ MultivariateBrownianMotion() [1/2]

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 \(\mathbf{X}(t_0) = \mathtt{x0}\).

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

◆ MultivariateBrownianMotion() [2/2]

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 \(\mathbf{X}(t_0) = \mathtt{x0}\).

The normal variates \(Z_j\) in are generated by gen.

Member Function Documentation

◆ getGen()

NormalGen getGen ( )

Returns the normal random variate generator used.

The RandomStream used for that generator can be changed via getGen().setStream(stream), for example.

◆ nextObservationVector() [1/4]

void nextObservationVector ( double []  obs)

Generates and returns in obs the next observation \(\mathbf{X}(t_j)\) of the multivariate stochastic process.

The processe is sampled sequentially, i.e. if the last observation generated was for time \(t_{j-1}\), the next observation returned will be for time \(t_j\).

◆ nextObservationVector() [2/4]

double [] nextObservationVector ( )

Generates and returns the next observation \(\mathbf{X}(t_j)\) of the multivariate stochastic process in a vector created automatically.

The processe is sampled sequentially, i.e. if the last observation generated was for time \(t_{j-1}\), the next observation returned will be for time \(t_j\).

◆ nextObservationVector() [3/4]

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 \(X(t_j)\).

Warning : This method will reset the observations time \(t_{j+1}\) for this process to nextTime. The user must make sure that the \(t_{j+1}\) supplied is \(\geq t_j\).

◆ nextObservationVector() [4/4]

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.

Uses the process parameters specified in the constructor. Note that this method does not affect the sample path of the process stored internally (if any).

◆ setParams() [1/2]

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.

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.

◆ setParams() [2/2]

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 \(\sigma= \mathtt{sigma}\).

Warning: This method will recompute some quantities stored internally, which may be slow if called too frequently.


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