RandomWalk¶
(Source code, png, hires.png, pdf)

class
RandomWalk
(*args)¶ Random walk process.
Parameters:  origin :
Point
Origin of the random walk.
 distribution :
Distribution
Distribution of dimension equal to the dimension of origin.
 timeGrid :
TimeGrid
, optional The time grid of the process. By default, the time grid is reduced to one time stamp equal to 0.
Notes
A random walk is a process where discretized on the time grid such that:
where and is a white noise of dimension .
Examples
Create a random walk:
>>> import openturns as ot >>> myTimeGrid = ot.RegularGrid(0, 0.1, 10) >>> myDist = ot.ComposedDistribution([ot.Normal(), ot.Exponential(0.2)], ot.ClaytonCopula(0.5)) >>> myOrigin = ot.Point(myDist.getMean()) >>> myRandomWalk = ot.RandomWalk(myOrigin, myDist, myTimeGrid)
Get a realization:
>>> myReal = myRandomWalk.getRealization()
Methods
getClassName
()Accessor to the object’s name. getContinuousRealization
()Get a continuous realization. getCovarianceModel
()Accessor to the covariance model. getDescription
()Get the description of the process. getDistribution
()Accessor to the distribution. getFuture
(*args)Prediction of the future iterations of the process. getId
()Accessor to the object’s id. getInputDimension
()Get the dimension of the domain . getMarginal
(indices)Get the marginal of the random process. getMesh
()Get the mesh. getName
()Accessor to the object’s name. getOrigin
()Accessor to the origin. getOutputDimension
()Get the dimension of the domain . getRealization
()Get a realization of the process. getSample
(size)Get realizations of the process. getShadowedId
()Accessor to the object’s shadowed id. getTimeGrid
()Get the time grid of observation of the process. getTrend
()Accessor to the trend. getVisibility
()Accessor to the object’s visibility state. hasName
()Test if the object is named. hasVisibleName
()Test if the object has a distinguishable name. isComposite
()Test whether the process is composite or not. isNormal
()Test whether the process is normal or not. isStationary
()Test whether the process is stationary or not. setDescription
(description)Set the description of the process. setDistribution
(distribution)Accessor to the distribution. setMesh
(mesh)Set the mesh. setName
(name)Accessor to the object’s name. setOrigin
(origin)Accessor to the origin. setShadowedId
(id)Accessor to the object’s shadowed id. setTimeGrid
(timeGrid)Set the time grid of observation of the process. setVisibility
(visible)Accessor to the object’s visibility state. 
__init__
(*args)¶ Initialize self. See help(type(self)) for accurate signature.

getClassName
()¶ Accessor to the object’s name.
Returns:  class_name : str
The object class name (object.__class__.__name__).

getContinuousRealization
()¶ Get a continuous realization.
Returns:  realization :
Function
According to the process, the continuous realizations are built:
 either using a dedicated functional model if it exists: e.g. a functional basis process.
 or using an interpolation from a discrete realization of the process on : in dimension , a linear interpolation and in dimension , a piecewise constant function (the value at a given position is equal to the value at the nearest vertex of the mesh of the process).
 realization :

getCovarianceModel
()¶ Accessor to the covariance model.
Returns:  cov_model :
CovarianceModel
Covariance model, if any.
 cov_model :

getDescription
()¶ Get the description of the process.
Returns:  description :
Description
Description of the process.
 description :

getDistribution
()¶ Accessor to the distribution.
Returns:  distribution :
Distribution
The distribution of dimension of the white noise.
 distribution :

getFuture
(*args)¶ Prediction of the future iterations of the process.
Parameters:  stepNumber : int,
Number of future steps.
 size : int, , optional
Number of futures needed. Default is 1.
Returns:  prediction :
ProcessSample
orTimeSeries
future iterations of the process. If , prediction is a
TimeSeries
. Otherwise, it is aProcessSample
.

getId
()¶ Accessor to the object’s id.
Returns:  id : int
Internal unique identifier.

getInputDimension
()¶ Get the dimension of the domain .
Returns:  n : int
Dimension of the domain : .

getMarginal
(indices)¶ Get the marginal of the random process.
Parameters:  k : int or list of ints
Index of the marginal(s) needed.
Returns:  marginals :
Process
Process defined with marginal(s) of the random process.

getName
()¶ Accessor to the object’s name.
Returns:  name : str
The name of the object.

getOutputDimension
()¶ Get the dimension of the domain .
Returns:  d : int
Dimension of the domain .

getRealization
()¶ Get a realization of the process.
Returns:  realization :
Field
Contains a mesh over which the process is discretized and the values of the process at the vertices of the mesh.
 realization :

getSample
(size)¶ Get realizations of the process.
Parameters:  n : int,
Number of realizations of the process needed.
Returns:  processSample :
ProcessSample
realizations of the random process. A process sample is a collection of fields which share the same mesh .

getShadowedId
()¶ Accessor to the object’s shadowed id.
Returns:  id : int
Internal unique identifier.

getTimeGrid
()¶ Get the time grid of observation of the process.
Returns:  timeGrid :
RegularGrid
Time grid of a process when the mesh associated to the process can be interpreted as a
RegularGrid
. We check if the vertices of the mesh are scalar and are regularly spaced in but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).
 timeGrid :

getTrend
()¶ Accessor to the trend.
Returns:  trend :
TrendTransform
Trend, if any.
 trend :

getVisibility
()¶ Accessor to the object’s visibility state.
Returns:  visible : bool
Visibility flag.

hasName
()¶ Test if the object is named.
Returns:  hasName : bool
True if the name is not empty.

hasVisibleName
()¶ Test if the object has a distinguishable name.
Returns:  hasVisibleName : bool
True if the name is not empty and not the default one.

isComposite
()¶ Test whether the process is composite or not.
Returns:  isComposite : bool
True if the process is composite (built upon a function and a process).

isNormal
()¶ Test whether the process is normal or not.
Returns:  isNormal : bool
True if the process is normal.
Notes
A stochastic process is normal if all its finite dimensional joint distributions are normal, which means that for all and , with , there is and such that:
where , and and is the symmetric matrix:
A Gaussian process is entirely defined by its mean function and its covariance function (or correlation function ).

isStationary
()¶ Test whether the process is stationary or not.
Returns:  isStationary : bool
True if the process is stationary.
Notes
A process is stationary if its distribution is invariant by translation: , , , we have:

setDescription
(description)¶ Set the description of the process.
Parameters:  description : sequence of str
Description of the process.

setDistribution
(distribution)¶ Accessor to the distribution.
Parameters:  distribution :
Distribution
The distribution of dimension of the white noise.
 distribution :

setName
(name)¶ Accessor to the object’s name.
Parameters:  name : str
The name of the object.

setOrigin
(origin)¶ Accessor to the origin.
Parameters:  origin :
Point
The origin of the random walk.
 origin :

setShadowedId
(id)¶ Accessor to the object’s shadowed id.
Parameters:  id : int
Internal unique identifier.

setTimeGrid
(timeGrid)¶ Set the time grid of observation of the process.
Returns:  timeGrid :
RegularGrid
Time grid of observation of the process when the mesh associated to the process can be interpreted as a
RegularGrid
. We check if the vertices of the mesh are scalar and are regularly spaced in but we don’t check if the connectivity of the mesh is conform to the one of a regular grid (without any hole and composed of ordered instants).
 timeGrid :

setVisibility
(visible)¶ Accessor to the object’s visibility state.
Parameters:  visible : bool
Visibility flag.
 origin :