This class represents an Ornstein-Uhlenbeck process as in OrnsteinUhlenbeckProcess, but the process is generated using the simple Euler scheme. More...
Public Member Functions | |
| OrnsteinUhlenbeckProcessEuler (double x0, double alpha, double b, double sigma, RandomStream stream) | |
Constructor with parameters \(\alpha=\) alpha, \(b\), \(\sigma=\) sigma and initial value \(X(t_0) =\) x0. More... | |
| OrnsteinUhlenbeckProcessEuler (double x0, double alpha, double b, double sigma, NormalGen gen) | |
| Here, the normal variate generator is specified directly instead of specifying the stream. 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 and returns an observation of the process in dt time units, assuming that the process has value \(x\) at the current time. More... | |
| double [] | generatePath () |
Generates a sample path of the process at all observation times, which are provided in array t. More... | |
 Public Member Functions inherited from OrnsteinUhlenbeckProcess | |
| OrnsteinUhlenbeckProcess (double x0, double alpha, double b, double sigma, RandomStream stream) | |
Constructs a new OrnsteinUhlenbeckProcess with parameters \(\alpha=\) alpha, \(b\), \(\sigma=\) sigma and initial value \(X(t_0) =\) x0. More... | |
| OrnsteinUhlenbeckProcess (double x0, double alpha, double b, double sigma, NormalGen gen) | |
| Here, the normal variate generator is specified directly instead of specifying the stream. More... | |
| double | nextObservation () |
| double | nextObservation (double nextTime) |
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 \(X(t_j)\). 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 (RandomStream stream) |
Generates a sample path of the process at all observation times, which are provided in array t. More... | |
| void | setParams (double x0, double alpha, double b, double sigma) |
Resets the parameters \(X(t_0) =\) x0, \(\alpha=\) alpha, \(b =\) b and \(\sigma=\) 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 | getAlpha () |
| Returns the value of \(\alpha\). | |
| double | getB () |
| Returns the value of \(b\). | |
| 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 | initArrays (int d) |
| Protected Member Functions inherited from OrnsteinUhlenbeckProcess | |
| void | initArrays (int d) |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
Additional Inherited Members | |
| Protected Attributes inherited from OrnsteinUhlenbeckProcess | |
| NormalGen | gen |
| double | alpha |
| double [] | badt |
| 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 inherited from OrnsteinUhlenbeckProcess | |
| double | beta |
| double | sigma |
| double [] | alphadt |
| double [] | sigmasqrdt |
Detailed Description
This class represents an Ornstein-Uhlenbeck process as in OrnsteinUhlenbeckProcess, but the process is generated using the simple Euler scheme.
\[ X(t_j) - X(t_{j-1}) = \alpha(b - X(t_{j-1}))(t_j - t_{j-1}) + \sigma\sqrt{t_j - t_{j-1}} Z_j \tag{ornstein-seqEuler} \]
where \(Z_j \sim N(0,1)\). This is a good approximation only for small time intervals \(t_j - t_{j-1}\).
Constructor & Destructor Documentation
◆ OrnsteinUhlenbeckProcessEuler() [1/2]
| OrnsteinUhlenbeckProcessEuler | ( | double | x0, |
| double | alpha, | ||
| double | b, | ||
| double | sigma, | ||
| RandomStream | stream | ||
| ) |
Constructor with parameters \(\alpha=\) alpha, \(b\), \(\sigma=\) sigma and initial value \(X(t_0) =\) x0.
The normal variates \(Z_j\) will be generated by inversion using the stream stream.
◆ OrnsteinUhlenbeckProcessEuler() [2/2]
| 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.
Member Function Documentation
◆ generatePath()
| 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).
◆ nextObservation() [1/2]
| double nextObservation | ( | double | nextTime | ) |
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 \(\geq t_j\).
◆ nextObservation() [2/2]
| 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).
The documentation for this class was generated from the following file:
- OrnsteinUhlenbeckProcessEuler.java
