aleatory

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Overview

The aleatory (/ˈeɪliətəri/) Python library provides functionality for simulating and visualising stochastic processes. More precisely, it introduces objects representing a number of stochastic processes 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 stochastic processes in one dimension:

• Arithmetic Brownian Motion (see Brownian Motion)
• Bessel process
• Brownian Bridge
• Brownian Excursion
• Brownian Meander
• Brownian Motion
• Constant Elasticity Variance (CEV) process
• Cox–Ingersoll–Ross (CIR) process
• Chan-Karolyi-Longstaff-Sanders (CKLS) process
• Fractional Brownian Motion process
• Galton-Watson process with Poisson branching
• Gamma process
• Gaussian Process with Constant Kernel
• Gaussian Process with Linear Kernel
• Gaussian Process with Matern Kernel
• Gaussian Process with Periodic Kernel
• Gaussian Process with RBF Kernel
• Gaussian Process with Squared Exponential Kernel
• General Random Walk
• Geometric Brownian Motion
• Hawkes process
• Inverse Gaussian process
• Inhomogeneous Poisson process
• Mixed Poisson process
• Ornstein–Uhlenbeck (OU) process
• Poisson process
• Random Walk
• Squared Bessel processes
• Vasicek process
• Variance-Gamma process
• White Noise

From v1.1.1 aleatory supports the following 2-d stochastic processes:

• Brownian Motion 2D
• Correlated Brownian Motions
• Random Walk 2D

Installation

Aleatory is available on pypi and can be installed as follows

pip install aleatory

Dependencies

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

Compatibility

Aleatory is tested on Python versions 3.8, 3.9, 3.10, and 3.11

Quick-Start

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 examples visit the Quick-Start Guide.

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