StochasticProcess (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.stochprocess.StochasticProcess

Direct Known Subclasses:

BrownianMotion, CIRProcess, CIRProcessEuler, GammaProcess, GeometricBrownianMotion, GeometricLevyProcess, GeometricVarianceGammaProcess, InverseGaussianProcess, NormalInverseGaussianProcess, OrnsteinUhlenbeckProcess, VarianceGammaProcess
```
public abstract class StochasticProcess
extends java.lang.Object
```
Abstract base class for a stochastic process {X(t) : t >= 0} sampled (or observed) at a finite number of time points, 0 = t₀ < t₁ < ^... < t_d. The observation times are usually all specified before generating a sample path. This can be done via setObservationTimes. The method generatePath generates X(t₁),..., X(t_d) and memorizes them in a vector, which can be recovered by getPath.
Alternatively, for some types of processes, the observations X(t_j) can be generated sequentially, one at a time, by invoking resetStartProcess first, and then nextObservation repeatedly. For some types of processes, the observation times can be specified one by one as well, when generating the path. This may be convenient or even necessary if the observation times are random, for example.
WARNING: After having called the constructor for one of the subclass, one must always set the observation times of the process, by calling method setObservationTimes for example or otherwise.

Field Summary

Fields
Modifier and Type Field and Description

double[] path

Fields
Modifier and Type	Field and Description
`double[]`	`path`

Constructor Summary

Constructors
Constructor and Description

StochasticProcess()

Constructors
Constructor and Description
`StochasticProcess()`

Method Summary

Methods
Modifier and Type	Method and Description
`abstract double[]`	`generatePath()` Generates, returns, and saves the sample path {X(t₀), X(t₁),…, X(t_d)}.
`double[]`	`generatePath(RandomStream stream)` Same as `generatePath()`, but first resets the stream to `stream`.
`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.
`double`	`getCurrentObservation()` Returns the value of the last generated observation X(t_j).
`int`	`getCurrentObservationIndex()` Returns the value of the index j corresponding to the time t_j of the last generated observation.
`int`	`getNbObservationTimes()` Returns the number of observation times excluding the time t₀.
`double`	`getObservation(int j)` Returns X(t_j) from the current sample path.
`double[]`	`getObservationTimes()` Returns a reference to the array that contains the observation times (t₀,..., t_d).
`double[]`	`getPath()` Returns a reference to the last generated sample path {X(t₀),..., X(t_d)}.
`abstract RandomStream`	`getStream()` Returns the random stream of the underlying generator.
`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 j are in the array `pathIndices`.
`double`	`getX0()` Returns the initial value X(t₀) for this process.
`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`.
`double`	`nextObservation()` Generates and returns the next observation X(t_j) of the stochastic process.
`void`	`resetStartProcess()` Resets the observation counter to its initial value j = 0, so that the current observation X(t_j) becomes X(t₀).
`void`	`setObservationTimes(double[] T, int d)` Sets the observation times of the process to a copy of `T`, with t₀ = `T[0]` and t_d = `T[d]`.
`void`	`setObservationTimes(double delta, int d)` Sets equidistant observation times at t_j = jδ, for j = 0,..., d, and `delta` = δ.
`abstract void`	`setStream(RandomStream stream)` Resets the random stream of the underlying generator to `stream`.
`void`	`setX0(double s0)` Sets the initial value X(t₀) for this process to `s0`, and reinitializes.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - path
```
public double[] path
```
- Constructor Detail
  - StochasticProcess
```
public StochasticProcess()
```
- Method Detail
  - setObservationTimes
```
public void setObservationTimes(double[] T,
                       int d)
```
    Sets the observation times of the process to a copy of T, with t₀ = T[0] and t_d = T[d]. The size of T must be d + 1.
  - setObservationTimes
```
public void setObservationTimes(double delta,
                       int d)
```
    Sets equidistant observation times at t_j = jδ, for j = 0,..., d, and delta = δ.
  - getObservationTimes
```
public double[] getObservationTimes()
```
    Returns a reference to the array that contains the observation times (t₀,..., t_d). Warning: This method should only be used to read the observation times. Changing the values in the array directly may have unexpected consequences. The method setObservationTimes should be used to modify the observation times.
  - getNbObservationTimes
```
public int getNbObservationTimes()
```
    Returns the number of observation times excluding the time t₀.
  - generatePath
```
public abstract double[] generatePath()
```
    Generates, returns, and saves the sample path {X(t₀), X(t₁),…, X(t_d)}. It can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type.
  - generatePath
```
public double[] generatePath(RandomStream stream)
```
    Same as generatePath(), but first resets the stream to stream.
  - getPath
```
public double[] getPath()
```
    Returns a reference to the last generated sample path {X(t₀),..., X(t_d)}. Warning: The returned array and its size should not be modified, because this is the one that memorizes the observations (not a copy of it). To obtain a copy, use getSubpath instead.
  - getSubpath
```
public 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 j are in the array pathIndices. The size of pathIndices should be at least as much as that of subpath.
  - getObservation
```
public double getObservation(int j)
```
    Returns X(t_j) from the current sample path. Warning: If the observation X(t_j) for the current path has not yet been generated, then the value returned is unpredictable.
  - resetStartProcess
```
public void resetStartProcess()
```
    Resets the observation counter to its initial value j = 0, so that the current observation X(t_j) becomes X(t₀). This method should be invoked before generating observations sequentially one by one via nextObservation, for a new sample path.
  - hasNextObservation
```
public 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. Otherwise returns false.
  - nextObservation
```
public double nextObservation()
```
    Generates and returns the next observation X(t_j) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time t_j-1, the next observation returned will be for time t_j. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the t_j's is then specified by the subclass. All the processes generated using principal components analysis (PCA) do not have this method.
  - getCurrentObservationIndex
```
public int getCurrentObservationIndex()
```
    Returns the value of the index j corresponding to the time t_j of the last generated observation.
  - getCurrentObservation
```
public double getCurrentObservation()
```
    Returns the value of the last generated observation X(t_j).
  - getX0
```
public double getX0()
```
    Returns the initial value X(t₀) for this process.
  - setX0
```
public void setX0(double s0)
```
    Sets the initial value X(t₀) for this process to s0, and reinitializes.
  - setStream
```
public abstract void setStream(RandomStream stream)
```
    Resets the random stream of the underlying generator to stream.
  - getStream
```
public abstract RandomStream getStream()
```
    Returns the random stream of the underlying generator.
  - getArrayMappingCounterToIndex
```
public 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. If this process is sampled sequentially, then this map is trivial (i.e. i_k = k). But it can be useful in a more general setting where the process is not sampled sequentially (for example, by a Brownian or gamma bridge) and one wants to know which observations of the current sample path were previously generated or will be generated next.

Class StochasticProcess

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

path

Constructor Detail

StochasticProcess

Method Detail

setObservationTimes

setObservationTimes

getObservationTimes

getNbObservationTimes

generatePath

generatePath

getPath

getSubpath

getObservation

resetStartProcess

hasNextObservation

nextObservation

getCurrentObservationIndex

getCurrentObservation

getX0

setX0

setStream

getStream

getArrayMappingCounterToIndex