SSJ
V. 2.6.

umontreal.iro.lecuyer.stochprocess
Class BrownianMotion

java.lang.Object
  extended by umontreal.iro.lecuyer.stochprocess.StochasticProcess
      extended by umontreal.iro.lecuyer.stochprocess.BrownianMotion
Direct Known Subclasses:
BrownianMotionBridge, BrownianMotionPCA, BrownianMotionPCAEqualSteps

public class BrownianMotion
extends StochasticProcess

This class represents a Brownian motion process {X(t) : t >= 0}, sampled at times 0 = t0 < t1 < ... < td. This process obeys the stochastic differential equation

dX(t) = μdt + σdB(t),

with initial condition X(0) = x0, where μ and σ are the drift and volatility parameters, and {B(t), t >= 0} is a standard Brownian motion (with drift 0 and volatility 1). This process has stationary and independent increments over disjoint time intervals (it is a Lévy process) and the increment over an interval of length t is normally distributed with mean μt and variance σ2t.

In this class, this process is generated using the sequential (or random walk) technique: X(0) = x0 and

X(tj) - X(tj-1) = μ(tj - tj-1) + σ(t_j - t_j-1)1/2Zj

where ZjN(0, 1).


Constructor Summary
BrownianMotion(double x0, double mu, double sigma, NormalGen gen)
          Constructs a new BrownianMotion with parameters μ = mu, σ = sigma and initial value X(t0) = x0.
BrownianMotion(double x0, double mu, double sigma, RandomStream stream)
          Constructs a new BrownianMotion with parameters μ = mu, σ = sigma and initial value X(t0) = x0.
 
Method Summary
 double[] generatePath()
          Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}.
 double[] generatePath(double[] uniform01)
          Same as generatePath(), but a vector of uniform random numbers must be provided to the method.
 double[] generatePath(RandomStream stream)
          Same as generatePath(), but first resets the stream to stream.
 NormalGen getGen()
          Returns the normal random variate generator used.
 double getMu()
          Returns the value of μ.
 double getSigma()
          Returns the value of σ.
 RandomStream getStream()
          Returns the random stream of the normal generator.
 double nextObservation()
          Generates and returns the next observation X(tj) of the stochastic process.
 double nextObservation(double nextTime)
          Generates and returns the next observation at time tj+1 = nextTime.
 double nextObservation(double x, double dt)
          Generates an observation of the process in dt time units, assuming that the process has value x at the current time.
 void setParams(double x0, double mu, double sigma)
          Resets the parameters X(t0) = x0, μ = mu and σ = sigma of the process.
 void setStream(RandomStream stream)
          Resets the random stream of the normal generator to stream.
 
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

BrownianMotion

public BrownianMotion(double x0,
                      double mu,
                      double sigma,
                      RandomStream stream)
Constructs a new BrownianMotion with parameters μ = mu, σ = sigma and initial value X(t0) = x0. The normal variates Zj in will be generated by inversion using stream.


BrownianMotion

public BrownianMotion(double x0,
                      double mu,
                      double sigma,
                      NormalGen gen)
Constructs a new BrownianMotion with parameters μ = mu, σ = sigma and initial value X(t0) = x0. Here, the normal variate generator NormalGen is specified directly instead of specifying the stream and using inversion. The normal generator gen can use another method than inversion.

Method Detail

nextObservation

public double nextObservation()
Description copied from class: StochasticProcess
Generates and returns the next observation X(tj) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time tj-1, the next observation returned will be for time tj. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the tj's is then specified by the subclass. All the processes generated using principal components analysis (PCA) do not have this method.

Overrides:
nextObservation in class StochasticProcess

nextObservation

public double nextObservation(double nextTime)
Generates and returns the next observation at time tj+1 = nextTime. It uses 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). Warning: This method will reset the observations time tj+1 for this process to nextTime. The user must make sure that the tj+1 supplied is  >= tj.


nextObservation

public double nextObservation(double x,
                              double dt)
Generates 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).


generatePath

public double[] generatePath()
Description copied from class: StochasticProcess
Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}. It can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type.

Specified by:
generatePath in class StochasticProcess

generatePath

public double[] generatePath(double[] uniform01)
Same as generatePath(), but a vector of uniform random numbers must be provided to the method. These uniform random numbers are used to generate the path.


generatePath

public double[] generatePath(RandomStream stream)
Description copied from class: StochasticProcess
Same as generatePath(), but first resets the stream to stream.

Overrides:
generatePath in class StochasticProcess

setParams

public void setParams(double x0,
                      double mu,
                      double sigma)
Resets the parameters X(t0) = x0, μ = mu and σ = sigma of the process. Warning: This method will recompute some quantities stored internally, which may be slow if called too frequently.


setStream

public void setStream(RandomStream stream)
Resets the random stream of the normal generator to stream.

Specified by:
setStream in class StochasticProcess

getStream

public RandomStream getStream()
Returns the random stream of the normal generator.

Specified by:
getStream in class StochasticProcess

getMu

public double getMu()
Returns the value of μ.


getSigma

public double getSigma()
Returns the value of σ.


getGen

public NormalGen getGen()
Returns the normal random variate generator used. The RandomStream used by that generator can be changed via getGen().setStream(stream), for example.


SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.