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java.lang.Object umontreal.iro.lecuyer.stochprocess.StochasticProcess umontreal.iro.lecuyer.stochprocess.BrownianMotion umontreal.iro.lecuyer.stochprocess.BrownianMotionBridge
public class BrownianMotionBridge
Represents a Brownian motion process {X(t) : t >= 0} sampled using the bridge sampling technique (see for example). This technique generates first the value X(t_{d}) at the last observation time, then the value at time t_{d/2} (or the nearest integer), then the values at time t_{d/4} and at time t_{3d/4} (or the nearest integers), and so on. If the process has already been sampled at times t_{i} < t_{k} but not in between, the next sampling point in that interval will be t_{j} where j = floor((i + k)/2). For example, if the sampling times used are { t_{0}, t_{1}, t_{2}, t_{3}, t_{4}, t_{5}}, then the observations are generated in the following order: X(t_{5}), X(t_{2}), X(t_{1}), X(t_{3}), X(t_{4}).
Warning:
Both the generatePath and the nextObservation methods from
BrownianMotion
are
modified to use the bridge method.
In the case of nextObservation, the user should understand
that the observations returned are not ordered chronologically.
However they will be once an entire path is generated and the observations
are read from the internal array (referenced by the getPath method)
that contains them.
The method nextObservation(double nextTime) differs from that of
the class
BrownianMotion
in that nextTime represents
the next observation time of the Brownian bridge.
However, the t_{i} supplied must still be nondecreasing with i.
Note also that, if the path is not entirely generated before being read from this array, there will be ``pollution'' from the previous path generated, and the observations will not represent a sample path of this process.
Constructor Summary  

BrownianMotionBridge(double x0,
double mu,
double sigma,
NormalGen gen)
Constructs a new BrownianMotionBridge with parameters μ = 

BrownianMotionBridge(double x0,
double mu,
double sigma,
RandomStream stream)
Constructs a new BrownianMotionBridge with parameters μ = 
Method Summary  

double[] 
generatePath()
Generates, returns, and saves the sample path {X(t_{0}), X(t_{1}),…, X(t_{d})}. 
double[] 
generatePath(double[] uniform01)
Same as generatePath(), but a vector of uniform random numbers must be provided to the method. 
double 
nextObservation()
Generates and returns the next observation X(t_{j}) of the stochastic process. 
double 
nextObservation(double nextTime)
Generates and returns the next observation at time t_{j+1} = nextTime. 
void 
resetStartProcess()
Resets the observation counter to its initial value j = 0, so that the current observation X(t_{j}) becomes X(t_{0}). 
Methods inherited from class umontreal.iro.lecuyer.stochprocess.BrownianMotion 

generatePath, getGen, getMu, getSigma, getStream, nextObservation, setParams, setStream 
Methods inherited from class umontreal.iro.lecuyer.stochprocess.StochasticProcess 

getArrayMappingCounterToIndex, getCurrentObservation, getCurrentObservationIndex, getNbObservationTimes, getObservation, getObservationTimes, getPath, getSubpath, getX0, hasNextObservation, setObservationTimes, setObservationTimes, setX0 
Methods inherited from class java.lang.Object 

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

public BrownianMotionBridge(double x0, double mu, double sigma, RandomStream stream)
RandomStream
stream.
public BrownianMotionBridge(double x0, double mu, double sigma, NormalGen gen)
NormalGen
gen.
Method Detail 

public double nextObservation()
StochasticProcess
nextObservation
in class BrownianMotion
public double nextObservation(double nextTime)
BrownianMotion
nextObservation
in class BrownianMotion
public double[] generatePath()
StochasticProcess
generatePath
in class BrownianMotion
public double[] generatePath(double[] uniform01)
BrownianMotion
generatePath
in class BrownianMotion
public void resetStartProcess()
StochasticProcess
nextObservation
, for a new sample path.
resetStartProcess
in class StochasticProcess

SSJ V. 2.6. 

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SUMMARY: NESTED  FIELD  CONSTR  METHOD  DETAIL: FIELD  CONSTR  METHOD 