.. _sphx_glr_api_gallery_probability_sde:

Stochastic differential equations
-----------------------------------

The Euler-Maruyama scheme, geometric Brownian motion, and the
Ornstein-Uhlenbeck process.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Itô (1944) gave meaning to dX = a\,dt + b\,dW when W is Brownian motion, whose paths have no derivative. His chain rule has an extra term: for geometric Brownian motion dX = \mu X\,dt + \sigma X\,dW it gives">

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  .. image:: /api/gallery/probability/sde/images/thumb/sphx_glr_plot_01_ito_euler_maruyama_thumb.png
    :alt:

  :doc:`/api/gallery/probability/sde/plot_01_ito_euler_maruyama`

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      <div class="sphx-glr-thumbnail-title">Itô calculus and the Euler-Maruyama scheme</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/probability/sde/plot_01_ito_euler_maruyama