.. only:: html

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

        Click :ref:`here <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
============================

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.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m
    ot.Log.Show(ot.Log.NONE)








Define the origin


.. code-block:: default

    origin = [0.0]








Define an 1-d mesh


.. code-block:: default

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








1-d random walk and discrete distribution


.. code-block:: default

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





1-d random walk and continuous distribution


.. code-block:: default

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





Define the origin


.. code-block:: default

    origin = [0.0]*2








color palette


.. code-block:: default

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








2-d random walk and discrete distribution


.. code-block:: default

    dist = ot.UserDefined([[-1., -2.], [1., 3.]], [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:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_random_walk_process_003.png
    :alt: 2D Random Walk with discrete steps
    :class: sphx-glr-single-img





2-d random walk and continuous distribution


.. code-block:: default

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






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.339 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_random_walk_process.py:


.. only :: html

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



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

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



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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_