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Stochastic Processes Simulation and Visualisation

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The aleatory (/ˈeɪliətəri/) Python library provides functionality for simulating and visualising stochastic processes. More precisely, it introduces objects representing a number of continuous-time stochastic processes $X = (X_t : t\geq 0)$ and provides methods to:

  • generate realizations/trajectories from each process —over discrete time sets
  • create visualisations to illustrate the processes properties and behaviour

Currently, aleatory supports the following processes:

  • Brownian Motion
  • Geometric Brownian Motion
  • Ornstein–Uhlenbeck
  • Vasicek
  • Cox–Ingersoll–Ross
  • Constant Elasticity
  • Bessel Process
  • Squared Bessel Processs


Aleatory is available on pypi and can be installed as follows

pip install aleatory


Aleatory relies heavily on

  • numpy for random number generation
  • scipy and statsmodels for support for a number of one-dimensional distributions.
  • matplotlib for creating visualisations


Aleatory is tested on Python versions 3.8, 3.9, and 3.10


Aleatory allows you to create fancy visualisations from different stochastic processes in an easy and concise way.

For example, the following code

from aleatory.processes import BrownianMotion

brownian = BrownianMotion()
brownian.draw(n=100, N=100, colormap="cool", figsize=(12,9))

generates a chart like this:

For more example visit the Quick-Start Guide.

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