# Package umontreal.iro.lecuyer.stochprocess

Class Summary Class Description BrownianMotion This class represents a Brownian motion process {*X*(*t*) :*t*>= 0}, sampled at times 0 =*t*_{0}<*t*_{1}<^{ ...}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 =*t*_{0}<*t*_{1}<^{ ...}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 =*t*_{0}<*t*_{1}<^{ ...}OrnsteinUhlenbeckProcessEuler .StochasticProcess Abstract base class for a stochastic process {*X*(*t*) :*t*>= 0} sampled (or observed) at a finite number of time points, 0 =*t*_{0}<*t*_{1}<^{ ...}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.

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