umontreal.iro.lecuyer.stochprocess

Class OrnsteinUhlenbeckProcessEuler

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.OrnsteinUhlenbeckProcess

umontreal.iro.lecuyer.stochprocess.OrnsteinUhlenbeckProcessEuler

public class OrnsteinUhlenbeckProcessEuler
extends OrnsteinUhlenbeckProcess

. This class represents an Ornstein-Uhlenbeck process as in OrnsteinUhlenbeckProcess, but the process is generated using the simple Euler scheme

X(t_j) - X(t_j-1) = α(b - X(t_j-1))(t_j - t_j-1) + σ(t_j - t_j-1)^1/2 Z_j

where Z_j∼N(0, 1). This is a good approximation only for small time intervals t_j - t_j-1.

Constructor Summary

Constructors

Constructor and Description
OrnsteinUhlenbeckProcessEuler(double x0, double alpha, double b, double sigma, NormalGen gen) Here, the normal variate generator is specified directly instead of specifying the stream.
OrnsteinUhlenbeckProcessEuler(double x0, double alpha, double b, double sigma, RandomStream stream) Constructor with parameters α = alpha, b, σ = sigma and initial value X(t0) = x0.

Method Summary

Modifier and Type	Method and Description
double[]	generatePath() Generates a sample path of the process at all observation times, which are provided in array t.
double	nextObservation() Generates and returns the next observation at time tj+1 = nextTime.
double	nextObservation(double nextTime) Generates and returns the next observation at time tj+1 = nextTime, using the previous observation time tj defined earlier (either by this method or by setObservationTimes), as well as the value of the previous observation X(tj).
double	nextObservation(double x, double dt) Generates and returns an observation of the process in dt time units, assuming that the process has value x at the current time.

Methods inherited from class umontreal.iro.lecuyer.stochprocess.OrnsteinUhlenbeckProcess

generatePath, getAlpha, getB, getGen, getSigma, getStream, setParams, setStream

Methods inherited from class umontreal.iro.lecuyer.stochprocess.StochasticProcess

getArrayMappingCounterToIndex, getCurrentObservation, getCurrentObservationIndex, getNbObservationTimes, getObservation, getObservationTimes, getPath, getSubpath, getX0, hasNextObservation, resetStartProcess, setObservationTimes, setObservationTimes, setX0

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

OrnsteinUhlenbeckProcessEuler

public OrnsteinUhlenbeckProcessEuler(double x0,
                                     double alpha,
                                     double b,
                                     double sigma,
                                     RandomStream stream)

Constructor with parameters α = alpha, b, σ = sigma and initial value X(t₀) = x0. The normal variates Z_j will be generated by inversion using the stream stream.

OrnsteinUhlenbeckProcessEuler

public OrnsteinUhlenbeckProcessEuler(double x0,
                                     double alpha,
                                     double b,
                                     double sigma,
                                     NormalGen gen)

Here, the normal variate generator is specified directly instead of specifying the stream. The normal generator gen can use another method than inversion.

Method Detail

nextObservation

public double nextObservation()

Generates and returns the next observation at time t_j+1 = nextTime. Assumes the previous observation time is 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 >= t_j.

Overrides:

nextObservation in class OrnsteinUhlenbeckProcess

nextObservation

public double nextObservation(double nextTime)

Description copied from class: OrnsteinUhlenbeckProcess

Generates and returns the next observation at time t_j+1 = 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 >= t_j.

Overrides:

nextObservation in class OrnsteinUhlenbeckProcess

nextObservation

public double nextObservation(double x,
                              double dt)

Generates and returns an observation of the process in dt time units, assuming that the process has 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).

Overrides:

nextObservation in class OrnsteinUhlenbeckProcess

generatePath

public double[] generatePath()

Generates a sample path of the process at all observation times, which are provided in array t. Note that t[0] should be the observation time of x0, the initial value of the process, and t[] should have at least d + 1 elements (see the setObservationTimes method).

Overrides:

generatePath in class OrnsteinUhlenbeckProcess