https://github.com/crflynn/stochastic

Generate realizations of stochastic processes in python.
https://github.com/crflynn/stochastic

probability stochastic stochastic-differential-equations stochastic-processes stochastic-simulation-algorithm stochastic-volatility-models

Last synced: 8 months ago
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Generate realizations of stochastic processes in python.

• Host: GitHub
• URL: https://github.com/crflynn/stochastic
• Owner: crflynn
• License: mit
• Created: 2017-02-17T01:54:16.000Z (almost 9 years ago)
• Default Branch: master
• Last Pushed: 2022-12-09T06:43:37.000Z (about 3 years ago)
• Last Synced: 2025-05-13T10:19:14.974Z (8 months ago)
• Topics: probability, stochastic, stochastic-differential-equations, stochastic-processes, stochastic-simulation-algorithm, stochastic-volatility-models
• Language: Python
• Homepage: http://stochastic.readthedocs.io/en/stable/
• Size: 3.73 MB
• Stars: 473
• Watchers: 14
• Forks: 86
• Open Issues: 14
• Metadata Files:
  • Readme: README.rst
  • Changelog: CHANGELOG.rst
  • License: LICENSE.txt

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README

          
stochastic

==========

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A python package for generating realizations of stochastic processes.

Installation

------------

The ``stochastic`` package is available on pypi and can be installed using pip

.. code-block:: shell

    pip install stochastic

Dependencies

~~~~~~~~~~~~

Stochastic uses ``numpy`` for many calculations and ``scipy`` for sampling

specific random variables.

Processes

---------

This package offers a number of common discrete-time, continuous-time, and

noise process objects for generating realizations of stochastic processes as

``numpy`` arrays.

The diffusion processes are approximated using the Euler–Maruyama method.

Here are the currently supported processes and their class references within

the package.

* stochastic.processes

    * continuous

        * BesselProcess

        * BrownianBridge

        * BrownianExcursion

        * BrownianMeander

        * BrownianMotion

        * CauchyProcess

        * FractionalBrownianMotion

        * GammaProcess

        * GeometricBrownianMotion

        * InverseGaussianProcess

        * MixedPoissonProcess

        * MultifractionalBrownianMotion

        * PoissonProcess

        * SquaredBesselProcess

        * VarianceGammaProcess

        * WienerProcess

    * diffusion

        * DiffusionProcess (generalized)

        * ConstantElasticityVarianceProcess

        * CoxIngersollRossProcess

        * ExtendedVasicekProcess

        * OrnsteinUhlenbeckProcess

        * VasicekProcess

    * discrete

        * BernoulliProcess

        * ChineseRestaurantProcess

        * DirichletProcess

        * MarkovChain

        * MoranProcess

        * RandomWalk

    * noise

        * BlueNoise

        * BrownianNoise

        * ColoredNoise

        * PinkNoise

        * RedNoise

        * VioletNoise

        * WhiteNoise

        * FractionalGaussianNoise

        * GaussianNoise

Usage patterns

--------------

Sampling

~~~~~~~~

To use ``stochastic``, import the process you want and instantiate with the

required parameters. Every process class has a ``sample`` method for generating

realizations. The ``sample`` methods accept a parameter ``n`` for the quantity

of steps in the realization, but others (Poisson, for instance) may take

additional parameters. Parameters can be accessed as attributes of the

instance.

.. code-block:: python

    from stochastic.processes.discrete import BernoulliProcess

    bp = BernoulliProcess(p=0.6)

    s = bp.sample(16)

    success_probability = bp.p

Continuous processes provide a default parameter, ``t``, which indicates the

maximum time of the process realizations. The default value is 1. The sample

method will generate ``n`` equally spaced increments on the

interval ``[0, t]``.

Sampling at specific times

~~~~~~~~~~~~~~~~~~~~~~~~~~

Some continuous processes also provide a ``sample_at()`` method, in which a

sequence of time values can be passed at which the object will generate a

realization. This method ignores the parameter, ``t``, specified on

instantiation.

.. code-block:: python

    from stochastic.processes.continuous import BrownianMotion

    bm = BrownianMotion(drift=1, scale=1, t=1)

    times = [0, 3, 10, 11, 11.2, 20]

    s = bm.sample_at(times)

Sample times

~~~~~~~~~~~~

Continuous processes also provide a method ``times()`` which generates the time

values (using ``numpy.linspace``) corresponding to a realization of ``n``

steps. This is particularly useful for plotting your samples.

.. code-block:: python

    import matplotlib.pyplot as plt

    from stochastic.processes.continuous import FractionalBrownianMotion

    fbm = FractionalBrownianMotion(hurst=0.7, t=1)

    s = fbm.sample(32)

    times = fbm.times(32)

    plt.plot(times, s)

    plt.show()

Specifying an algorithm

~~~~~~~~~~~~~~~~~~~~~~~

Some processes provide an optional parameter ``algorithm``, in which one can

specify which algorithm to use to generate the realization using the

``sample()`` or ``sample_at()`` methods. See the documentation for

process-specific implementations.

.. code-block:: python

    from stochastic.processes.noise import FractionalGaussianNoise

    fgn = FractionalGaussianNoise(hurst=0.6, t=1)

    s = fgn.sample(32, algorithm='hosking')