# Aleatory 0.1.2

There is a new release of aleatory available in PyPi.

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

Aleatory is an open source project hosted here: aleatory -Git Homepage. Full documentation is available to read here: aleatory 0.1.2 – Documentation.

## What is new?

Aleatory 0.1.2 now supports two additional processes

• Bessel Processes
• Squared Bessel Processes

Both of these are currently supported for integer dimension. The general case will be featured soon

Aleatory provides functionality to create simple plots showing paths from Bessel and Squared Bessel processes with only 3 lines of code! For example, her we create a Bessel process of dimension 3 over the interval $[0,1]$, and simulate $N=5$ paths each one with $n=100$ steps.

from aleatory.processes import BESProcess
bes = BESProcess(dim=3)
fig = bes.plot(n=100, N=5, figsize=(9, 6))

Besides, it allows you to create charts showing not only the simulated paths but also additional elements, which provide insights about the nature of the process.

In these examples you can see:

• Expectation of the marginal distributions, i.e., $\mathbb{E}[X_t]$ for each $t$ on the discretisation of $[0,T]$
• Histogram of the final distribution $X_T$
• Probability density function –or kernel density estimator if appropriate– of $X_T$
• Expectation of $X_T$
• Envelopes of probability

Take a look at the Quick-Start Guide for details about how to customise your charts with aleatory.

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