Ergodicity Library: A Python Toolkit for Stochastic-Process Simulation, Time-Average Diagnostics, and Agent-Based Experiments

TL;DR

Ergodicity Library is an open-source Python toolkit that simplifies the simulation, analysis, and experimentation of stochastic processes, especially focusing on non-ergodic and heavy-tailed dynamics.

Contribution

It integrates process definition, analysis, and agent-based experiments into a unified framework, reducing the need for ad hoc scripting in stochastic dynamics research.

Findings

Provides reproducible examples for heavy-tailed processes and Levy diagnostics.

Supports a wide range of stochastic process families and analysis workflows.

Facilitates agent-based experiments with an integrated Python toolkit.

Abstract

ergodicity is an open-source Python library for computational work on stochastic dynamics, with particular emphasis on non-ergodicity, time-average behavior, heavy-tailed processes, and decision making under uncertainty. The package brings together three layers that are often split across ad hoc scripts: process definitions and simulators, analysis and fitting tools, and agent-based experimentation. This article documents the implemented software rather than presenting new stochastic theory. We describe the package architecture, the supported process families, the analysis workflow, and the practical boundaries of the current implementation. We also provide fully reproducible examples covering heavy-tailed ensemble spread, multiplicative Levy growth diagnostics, adaptive memory mean reversion, preasymptotic fluctuation analysis, and partial stochastic differential equation simulation. The package is positioned as an integration layer on top of the scientific Python stack, reducing the amount of glue code required to move from process specification to diagnostics and comparative experiments.