.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/stochastic_processes/plot_random_walk_process.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py:


Create a random walk process
============================

.. GENERATED FROM PYTHON SOURCE LINES 6-24

This example details first how to create and manipulate a random walk.

A random walk :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` is a process
where :math:`\mathcal{D}=\mathbb{R}` discretized on the time grid :math:`(t_i)_{i \geq 0}` such
that:

.. math::
   \begin{aligned}
     X_{t_0} & = & \underline{x}_{t_0} \\
     \forall n>0,\: X_{t_n} & = & X_{t_{n-1}} + \varepsilon_{t_n}
   \end{aligned}

where :math:`\underline{x}_0 \in \mathbb{R}^d` and :math:`\varepsilon` is a white noise of
dimension :math:`d`.

The library proposes to model it through the object *RandomWalk* defined
thanks to the origin, the distribution of the white noise and the time
grid.

.. GENERATED FROM PYTHON SOURCE LINES 26-32

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

    ot.Log.Show(ot.Log.NONE)








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Define the origin

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.. code-block:: Python

    origin = [0.0]








.. GENERATED FROM PYTHON SOURCE LINES 37-38

Define an 1-d mesh

.. GENERATED FROM PYTHON SOURCE LINES 38-40

.. code-block:: Python

    tgrid = ot.RegularGrid(0.0, 1.0, 500)








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1-d random walk and discrete distribution

.. GENERATED FROM PYTHON SOURCE LINES 42-49

.. code-block:: Python

    dist = ot.UserDefined([[-1], [10]], [0.9, 0.1])
    process = ot.RandomWalk(origin, dist, tgrid)
    sample = process.getSample(5)
    graph = sample.drawMarginal(0)
    graph.setTitle("1D Random Walk with discrete steps")
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_001.png
   :alt: 1D Random Walk with discrete steps
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 50-51

1-d random walk and continuous distribution

.. GENERATED FROM PYTHON SOURCE LINES 51-58

.. code-block:: Python

    dist = ot.Normal(0.0, 1.0)
    process = ot.RandomWalk(origin, dist, tgrid)
    sample = process.getSample(5)
    graph = sample.drawMarginal(0)
    graph.setTitle("1D Random Walk with continuous steps")
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_002.png
   :alt: 1D Random Walk with continuous steps
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_002.png
   :class: sphx-glr-single-img





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Define the origin

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.. code-block:: Python

    origin = [0.0] * 2








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color palette

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.. code-block:: Python

    pal = ["red", "cyan", "blue", "yellow", "green"]








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2-d random walk and discrete distribution

.. GENERATED FROM PYTHON SOURCE LINES 68-76

.. code-block:: Python

    dist = ot.UserDefined([[-1.0, -2.0], [1.0, 3.0]], [0.5, 0.5])
    process = ot.RandomWalk(origin, dist, tgrid)
    sample = process.getSample(5)
    graph = ot.Graph("2D Random Walk with discrete steps", "X1", "X2", True)
    for i in range(5):
        graph.add(ot.Curve(sample[i], pal[i % len(pal)], "solid"))
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_003.png
   :alt: 2D Random Walk with discrete steps
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_003.png
   :class: sphx-glr-single-img





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2-d random walk and continuous distribution

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.. code-block:: Python

    dist = ot.Normal(2)
    process = ot.RandomWalk(origin, dist, tgrid)
    sample = process.getSample(5)
    graph = ot.Graph("2D Random Walk with continuous steps", "X1", "X2", True)
    for i in range(5):
        graph.add(ot.Curve(sample[i], pal[i % len(pal)], "solid"))
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_004.png
   :alt: 2D Random Walk with continuous steps
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_004.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_random_walk_process.ipynb <plot_random_walk_process.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_random_walk_process.py <plot_random_walk_process.py>`