Package umontreal.iro.lecuyer.stochprocess

This package provides classes to define stochastic processes {X(t), t≥0}, and to simulate their sample paths at a finite number of (discrete) observation times t₀≤t₁≤ ^...

See: Description

Class Summary

Class	Description
BrownianMotion	This class represents a Brownian motion process {X(t) : t >= 0}, sampled at times 0 = t0 < t1 < ...
BrownianMotionBridge	Represents a Brownian motion process {X(t) : t >= 0} sampled using the bridge sampling technique (see for example).
BrownianMotionPCA	A Brownian motion process {X(t) : t >= 0} sampled using the principal component decomposition (PCA).
BrownianMotionPCAEqualSteps	Same as BrownianMotionPCA, but uses a trick to speed up the calculation when the time steps are equidistant.
CIRProcess	This class represents a CIR (Cox, Ingersoll, Ross) process {X(t) : t >= 0}, sampled at times 0 = t0 < t1 < ...
CIRProcessEuler	.
GammaProcess	This class represents a gamma process {S(t) = G(t;μ, ν) : t >= 0} with mean parameter μ and variance parameter ν.
GammaProcessBridge	This class represents a gamma process {S(t) = G(t;μ, ν) : t >= 0} with mean parameter μ and variance parameter ν, sampled using the gamma bridge method (see for example).
GammaProcessPCA	Represents a gamma process sampled using the principal component analysis (PCA).
GammaProcessPCABridge	Same as GammaProcessPCA, but the generated uniforms correspond to a bridge transformation of the BrownianMotionPCA instead of a sequential transformation.
GammaProcessPCASymmetricalBridge	Same as GammaProcessPCABridge, but uses the fast inversion method for the symmetrical beta distribution, proposed by L'Ecuyer and Simard, to accelerate the generation of the beta random variables.
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.
GeometricBrownianMotion	.
GeometricLevyProcess	.
GeometricNormalInverseGaussianProcess	.
GeometricVarianceGammaProcess	This class represents a geometric variance gamma process S(t) (see).
InverseGaussianProcess	The inverse Gaussian process is a non-decreasing process where the increments are additive and are given by the inverse gaussian distribution, InverseGaussianDist.
InverseGaussianProcessBridge	Samples the path by bridge sampling: first finding the process value at the final time and then the middle time, etc.
InverseGaussianProcessMSH	Uses a faster generating method (MSH) than the simple inversion of the distribution function used by InverseGaussianProcess.
InverseGaussianProcessPCA	Approximates a principal component analysis (PCA) decomposition of the InverseGaussianProcess.
NormalInverseGaussianProcess	This class represents a normal inverse gaussian process (NIG).
OrnsteinUhlenbeckProcess	This class represents an Ornstein-Uhlenbeck process {X(t) : t >= 0}, sampled at times 0 = t0 < t1 < ...
OrnsteinUhlenbeckProcessEuler	.
StochasticProcess	Abstract base class for a stochastic process {X(t) : t >= 0} sampled (or observed) at a finite number of time points, 0 = t0 < t1 < ...
VarianceGammaProcess	This class represents a variance gamma (VG) process {S(t) = X(t;θ, σ, ν) : t >= 0}.
VarianceGammaProcessDiff	This class represents a variance gamma (VG) process {S(t) = X(t;θ, σ, ν) : t >= 0}.
VarianceGammaProcessDiffPCA	Same as VarianceGammaProcessDiff, but the two inner GammaProcess'es are of PCA type.
VarianceGammaProcessDiffPCABridge	Same as VarianceGammaProcessDiff, but the two inner GammaProcess'es are of the type PCABridge.
VarianceGammaProcessDiffPCASymmetricalBridge	Same as VarianceGammaProcessDiff, but the two inner GammaProcess'es are of the PCASymmetricalBridge type.

Package umontreal.iro.lecuyer.stochprocess Description

This package provides classes to define stochastic processes {X(t), t≥0}, and to simulate their sample paths at a finite number of (discrete) observation times t₀≤t₁≤ ^... ≤t_d. The observation of the generated path is thus the vector (X(t₀), X(t₁),..., X(t_d)).

The observation times t₀,..., 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.