SSJ  3.2.1
Stochastic Simulation in Java
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Classes
Package umontreal.ssj.stochprocess

Stochastic Processes. More...

Classes

class  BrownianMotion
 This class represents a Brownian motion process \(\{X(t) : t \geq0 \}\), sampled at times \(0 = t_0 < t_1 < \cdots< t_d\). More...
 
class  BrownianMotionBridge
 , then the observations are generated in the following order: \(X(t_5)\), \(X(t_2)\), \(X(t_1)\), \(X(t_3)\), \(X(t_4)\). More...
 
class  BrownianMotionPCA
 A Brownian motion process \(\{X(t) : t \geq0 \}\) sampled using the principal component decomposition (PCA) [63], [84], [133] . More...
 
class  BrownianMotionPCAEqualSteps
 Same as BrownianMotionPCA, but uses a trick to speed up the calculation when the time steps are equidistant. More...
 
class  CIRProcess
 This class represents a CIR (Cox, Ingersoll, Ross) process [32]  \(\{X(t) : t \geq0 \}\), sampled at times \(0 = t_0 < t_1 < \cdots< t_d\). More...
 
class  CIRProcessEuler
 This class represents a CIR process as in CIRProcess, but the process is generated using the simple Euler scheme. More...
 
class  GammaProcess
 This class represents a gamma process [144]  (page 82) \(\{ S(t) = G(t; \mu, \nu) : t \geq0 \}\) with mean parameter \(\mu\) and variance parameter \(\nu\). More...
 
class  GammaProcessBridge
 This class represents a gamma process \(\{ S(t) = G(t; \mu, \nu) : t \geq0 \}\) with mean parameter \(\mu\) and variance parameter \(\nu\), sampled using the gamma bridge method (see for example [177], [9] ). More...
 
class  GammaProcessPCA
 Represents a gamma process sampled using the principal component analysis (PCA). More...
 
class  GammaProcessPCABridge
 Same as GammaProcessPCA, but the generated uniforms correspond to a bridge transformation of the BrownianMotionPCA instead of a sequential transformation. More...
 
class  GammaProcessPCASymmetricalBridge
 Same as GammaProcessPCABridge, but uses the fast inversion method for the symmetrical beta distribution, proposed by L’Ecuyer and Simard [118] , to accelerate the generation of the beta random variables. More...
 
class  GammaProcessSymmetricalBridge
 This class differs from GammaProcessBridge only in that it requires the number of interval of the path to be a power of 2 and of equal size. More...
 
class  GeometricBrownianMotion
 Represents a geometric Brownian motion (GBM) process \(\{S(t), t\ge0\}\), which evolves according to the stochastic differential equation. More...
 
class  GeometricLevyProcess
 Abstract class used as a parent class for the exponentiation of a Lévy process \(X(t)\):

\[ S(t) = S(0) \exp\left(X(t) + (r - \omega_{RN}) t\right). \]

The interest is here denoted \(r\) and is refered to as muGeom in the class below. More...

 
class  GeometricNormalInverseGaussianProcess
 The geometric normal inverse gaussian (GNIG) process is the exponentiation of a NormalInverseGaussianProcess :

\[ S(t) = S_0 \exp\left[ (r-\omega_{RN})t + \mbox{NIG}(t;\alpha,\beta,\mu,\delta) \right], \]

where \(r\) is the interest rate. More...

 
class  GeometricVarianceGammaProcess
 This class represents a geometric variance gamma process \(S(t)\) (see [144]  (page 86)). More...
 
class  InverseGaussianProcess
 The inverse Gaussian process is a non-decreasing process where the increments are additive and are given by the inverse gaussian distribution, umontreal.ssj.probdist.InverseGaussianDist. More...
 
class  InverseGaussianProcessBridge
 Samples the path by bridge sampling: first finding the process value at the final time and then the middle time, etc. More...
 
class  InverseGaussianProcessMSH
 Uses a faster generating method (MSH) [153]  than the simple inversion of the distribution function used by InverseGaussianProcess. More...
 
class  InverseGaussianProcessPCA
 Approximates a principal component analysis (PCA) decomposition of the InverseGaussianProcess. More...
 
class  MultivariateBrownianMotion
 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...
 
class  MultivariateBrownianMotionBridge
 A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled via bridge sampling. More...
 
class  MultivariateBrownianMotionPCA
 A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled entirely using the principal component decomposition (PCA), as explained in [63] , page 92. More...
 
class  MultivariateBrownianMotionPCABigSigma
 A multivariate Brownian motion process \(\{\mathbf{X}(t) : t \geq0 \}\) sampled entirely using the principal component decomposition (PCA). More...
 
class  MultivariateGeometricBrownianMotion
 This class is a multivariate version of GeometricBrownianMotion. More...
 
class  MultivariateStochasticProcess
 This class is a multivariate version of StochasticProcess where the process evolves in the \(c\)-dimensional real space. More...
 
class  NormalInverseGaussianProcess
 This class represents a normal inverse gaussian process (NIG). More...
 
class  OrnsteinUhlenbeckProcess
 This class represents an Ornstein-Uhlenbeck process \(\{X(t) : t \geq0 \}\), sampled at times \(0 = t_0 < t_1 < \cdots< t_d\). More...
 
class  OrnsteinUhlenbeckProcessEuler
 This class represents an Ornstein-Uhlenbeck process as in OrnsteinUhlenbeckProcess, but the process is generated using the simple Euler scheme. More...
 
class  StochasticProcess
 Abstract base class for a stochastic process \(\{X(t) : t \geq0 \}\) sampled (or observed) at a finite number of time points, \(0 = t_0 < t_1 < \cdots< t_d\). More...
 
class  VarianceGammaProcess
 This class represents a variance gamma (VG) process \(\{S(t) = X(t; \theta, \sigma, \nu) : t \geq0\}\). More...
 
class  VarianceGammaProcessDiff
 This class represents a variance gamma (VG) process \(\{S(t) = X(t; \theta, \sigma, \nu) : t \geq0\}\). More...
 
class  VarianceGammaProcessDiffPCA
 Same as VarianceGammaProcessDiff, but the two inner GammaProcess ’es are of PCA type. More...
 
class  VarianceGammaProcessDiffPCABridge
 Same as VarianceGammaProcessDiff, but the two inner GammaProcess ’es are of the type PCABridge. More...
 
class  VarianceGammaProcessDiffPCASymmetricalBridge
 Same as VarianceGammaProcessDiff, but the two inner GammaProcess ’es are of the PCASymmetricalBridge type. More...
 

Detailed Description

Stochastic Processes.

This package provides classes to define stochastic processes \(\{X(t), t\ge0\}\), and to simulate their sample paths at a finite number of (discrete) observation times \(t_0 \le t_1 \le\cdots\le t_d\). The observation of the generated path is thus the vector \((X(t_0),X(t_1),…,X(t_d))\).

The observation times \(t_0, …, t_d\) can be specified (or changed) after defining the process, with the method setObservationTimes. The random stream used to generate the sample path can also be changed, using setStream.