Represents a Brownian motion process \(\{X(t) : t \geq0 \}\) sampled using the bridge sampling technique (see for example [69] ). More...
Public Member Functions | |
| BrownianMotionBridge (double x0, double mu, double sigma, RandomStream stream) | |
Constructs a new BrownianMotionBridge with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\) and initial value \(X(t_0) = \mathtt{x0}\). More... | |
| BrownianMotionBridge (double x0, double mu, double sigma, NormalGen gen) | |
Constructs a new BrownianMotionBridge with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\) and initial value \(X(t_0) = \mathtt{x0}\). More... | |
| double | nextObservation () |
| double | nextObservation (double nextTime) |
| double [] | generatePath () |
| double [] | generatePath (double[] uniform01) |
| void | resetStartProcess () |
 Public Member Functions inherited from BrownianMotion | |
| BrownianMotion (double x0, double mu, double sigma, RandomStream stream) | |
Constructs a new BrownianMotion with parameters \(\mu=\) mu, \(\sigma=\) sigma and initial value \(X(t_0) =\) x0. More... | |
| BrownianMotion (double x0, double mu, double sigma, NormalGen gen) | |
Constructs a new BrownianMotion with parameters \(\mu=\) mu, \(\sigma=\) sigma and initial value \(X(t_0) =\) x0. More... | |
| double | nextObservation () |
| double | nextObservation (double nextTime) |
Generates and returns the next observation at time \(t_{j+1} =\) nextTime. More... | |
| 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. More... | |
| double [] | generatePath () |
| double [] | generatePath (double[] uniform01) |
| Same as generatePath(), but a vector of uniform random numbers must be provided to the method. More... | |
| double [] | generatePath (RandomStream stream) |
| void | setParams (double x0, double mu, double sigma) |
| Resets the parameters \(X(t_0) = \mathtt{x0}\), \(\mu= \mathtt{mu}\) and \(\sigma= \mathtt{sigma}\) of the process. More... | |
| void | setStream (RandomStream stream) |
Resets the random stream of the normal generator to stream. | |
| RandomStream | getStream () |
| Returns the random stream of the normal generator. | |
| double | getMu () |
| Returns the value of \(\mu\). | |
| double | getSigma () |
| Returns the value of \(\sigma\). | |
| NormalGen | getGen () |
| Returns the normal random variate generator used. More... | |
| Public Member Functions inherited from StochasticProcess | |
| void | setObservationTimes (double[] T, int d) |
Sets the observation times of the process to a copy of T, with. More... | |
| void | setObservationTimes (double delta, int d) |
| Sets equidistant observation times at \(t_j = j\delta\), for. More... | |
| double [] | getObservationTimes () |
| Returns a reference to the array that contains the observation times. More... | |
| int | getNumObservationTimes () |
| Returns the number \(d\) of observation times, excluding the time \(t_0\). | |
| abstract double [] | generatePath () |
| Generates, returns, and saves the sample path \(\{X(t_0), X(t_1), \dots, X(t_d)\}\). More... | |
| double [] | generatePath (RandomStream stream) |
Same as generatePath(), but first resets the stream to stream. | |
| double [] | getPath () |
| Returns a reference to the last generated sample path \(\{X(t_0), ... , X(t_d)\}\). More... | |
| void | getSubpath (double[] subpath, int[] pathIndices) |
Returns in subpath the values of the process at a subset of the observation times, specified as the times \(t_j\) whose indices. More... | |
| double | getObservation (int j) |
| Returns \(X(t_j)\) from the current sample path. More... | |
| void | resetStartProcess () |
| Resets the observation counter to its initial value \(j=0\), so that the current observation \(X(t_j)\) becomes \(X(t_0)\). More... | |
| boolean | hasNextObservation () |
Returns true if \(j<d\), where \(j\) is the number of observations of the current sample path generated since the last call to resetStartProcess. More... | |
| double | nextObservation () |
| Generates and returns the next observation \(X(t_j)\) of the stochastic process. More... | |
| int | getCurrentObservationIndex () |
| Returns the value of the index \(j\) corresponding to the time. More... | |
| double | getCurrentObservation () |
| Returns the value of the last generated observation \(X(t_j)\). | |
| double | getX0 () |
| Returns the initial value \(X(t_0)\) for this process. | |
| void | setX0 (double s0) |
Sets the initial value \(X(t_0)\) for this process to s0, and reinitializes. | |
| abstract void | setStream (RandomStream stream) |
Resets the random stream of the underlying generator to stream. | |
| abstract RandomStream | getStream () |
| Returns the random stream of the underlying generator. | |
| int [] | getArrayMappingCounterToIndex () |
| Returns a reference to an array that maps an integer \(k\) to \(i_k\), the index of the observation \(S(t_{i_k})\) corresponding to the \(k\)-th observation to be generated for a sample path of this process. More... | |
Protected Member Functions | |
| void | init () |
| Protected Member Functions inherited from BrownianMotion | |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
Protected Attributes | |
| int | bridgeCounter = -1 |
| double [] | wMuDt |
| int [] | wIndexList |
| Protected Attributes inherited from BrownianMotion | |
| NormalGen | gen |
| double | mu |
| double [] | mudt |
| Protected Attributes inherited from StochasticProcess | |
| boolean | observationTimesSet = false |
| double | x0 = 0.0 |
| int | d = -1 |
| int | observationIndex = 0 |
| int | observationCounter = 0 |
| double [] | t |
| double [] | path |
| int [] | observationIndexFromCounter |
Package Attributes | |
| double [] | wSqrtDt |
| int [] | ptIndex |
| Package Attributes inherited from BrownianMotion | |
| double | sigma |
| double [] | sigmasqrdt |
Detailed Description
Represents a Brownian motion process \(\{X(t) : t \geq0 \}\) sampled using the bridge sampling technique (see for example [69] ).
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 \(j = \lfloor(i + k)/2 \rfloor\). 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 umontreal.ssj.stochprocess.BrownianMotion are modified to use the bridge method.
- Remarks
- From Pierre: Not sure if we should keep the
nextObservationmethods here. Normally, one should usegeneratePath.
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 umontreal.ssj.stochprocess.BrownianMotion in that nextTime represents the next observation time of the Brownian bridge. However, the \(t_i\) supplied must still be non-decreasing 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 & Destructor Documentation
◆ BrownianMotionBridge() [1/2]
| BrownianMotionBridge | ( | double | x0, |
| double | mu, | ||
| double | sigma, | ||
| RandomStream | stream | ||
| ) |
Constructs a new BrownianMotionBridge with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\) and initial value \(X(t_0) = \mathtt{x0}\).
The normal variates will be generated by inversion using the umontreal.ssj.rng.RandomStream stream.
◆ BrownianMotionBridge() [2/2]
| BrownianMotionBridge | ( | double | x0, |
| double | mu, | ||
| double | sigma, | ||
| NormalGen | gen | ||
| ) |
Constructs a new BrownianMotionBridge with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\) and initial value \(X(t_0) = \mathtt{x0}\).
The normal variates will be generated by the umontreal.ssj.randvar.NormalGen gen.
The documentation for this class was generated from the following file:
- BrownianMotionBridge.java
