ergodicity 0.3.1

A Python library for the applications of ergodicity economics toolkit

Ergodicity Library

Overview

The Ergodicity Library is a Python-based open-source library focused on the study of stochastic processes, ergodicity, and time-average behaviors. Initially inspired by the work of Ole Peters and Alexander Adamou in Ergodicity Economics, the library extends far beyond economics and can be applied in fields such as biology, physics, finance, and more. It provides tools for simulating and analyzing stochastic processes, with a particular focus on processes with heavy tails, and enables research on non-ergodic dynamics.

Key Features

• Stochastic Process Simulation: Includes a wide variety of stochastic processes, including Brownian motion, Lévy processes, and fractional Brownian motion.
• Ergodicity Research: Tools for studying ergodicity and time-average behavior of stochastic processes.
• Artificial Agents: Evolutionary algorithms and machine learning models for training agents to make decisions under uncertainty.
• Heavy-Tailed Processes: Special focus on processes with heavy-tailed distributions, such as Lévy alpha-stable processes.
• Symbolic Computations: Powerful tools for solving stochastic differential equations (SDEs) both numerically and symbolically.
• Parallel Processing: Support for multiprocessing to handle large-scale simulations efficiently.
• Visualization: Dynamic visualization of stochastic processes, with support for 3D interactive graphs.

Installation

To install the Ergodicity Library, you can clone the repository from GitHub:

git clone https://github.com/Kendiukhov/ergodicity_library.git
cd ergodicity-library
pip install -r requirements.txt

The library relies on widely used Python libraries like numpy, matplotlib, scipy, tensorflow, and keras.

Getting Started

Programming Prerequisites

• Basic knowledge of Python
• Familiarity with scientific libraries: NumPy, SymPy, Matplotlib
• Optional: TensorFlow and Keras for machine learning components

Academic Prerequisites

A basic understanding of the following topics is recommended:

• Probability theory and stochastic processes
• Ito calculus and stochastic differential equations (SDEs)
• Statistical estimation and fitting

Example

Here is a simple example to get started with simulating a Brownian motion process:

from ergodicity.process.basic import BrownianMotion

# Create a Brownian motion process
bm = BrownianMotion()

# Simulate the process
realization = bm.simulate(t=10, timestep=0.1 num_instance=1000, plot=True)

Documentation

Extensive documentation, examples, and tutorials are available at the Ergodicity Library website: https://ergodicitylibrary.com.

The documentation is also available on GitHub: https://kendiukhov.github.io/ergodicity_library.

Structure

The library is structured into three main modules:

1. Processes: Provides the core stochastic processes such as Brownian motion, Poisson processes, Lévy processes, and custom-defined processes.

   • Submodules:
     • basic.py: Core stochastic processes.
     • multiplicative.py: Processes with multiplicative dynamics.
     • with_memory.py: Stochastic processes with memory.
     • increments.py: Defines various stochastic differentials.
     • lib.py: Additional less common processes.
     • constructor.py: Allows creating new processes without programming.
     • custom_classes.py: Facilitates creating new process classes.
     • default_values.py: Contains default process parameters.
     • definitions.py: Core of the library, containing abstract classes and methods.
     • discrete.py: Handles discrete stochastic processes.

2. Tools: Functions for computation, analysis, and symbolic/numerical solutions for stochastic processes.

   • Submodules:
     • compute.py: Functions for calculating parameters of stochastic processes.
     • evaluate.py: Evaluates time-series data.
     • fit.py: Fits data to various distributions.
     • solve.py: Symbolic solutions for stochastic analysis problems.
     • multiprocessing.py: Supports multi-core computations.
     • automate.py: Automates research calls for comparative results.
     • preasymptotics.py: Analyzes pre-asymptotic behavior of processes.
     • research.py: Automated research pipelines.
     • partial_sde.py: Numerical simulations of partial stochastic differential equations.
     • helper.py: Auxiliary functions for different parts of the tools module.

3. Agents: Tools to create and train artificial agents using evolutionary algorithms and machine learning models.

   • Submodules:
     • agents.py: Initializes artificial agents and elementary algorithms for training.
     • agent_pool.py: Manages ensembles of interacting agents.
     • evaluation.py: Tool for analyzing agent behavior and utility functions.
     • evolutionary_nn.py: Implements evolutionary training for agent neural networks.
     • sml.py: Standard machine learning algorithms for training agents.
     • portfolio.py: Simulates portfolios of stochastic processes.
     • probability_weighting.py: Implements probability weighting functions for decision making.

Additionally, the library contains the following components:

• developer_tools: Tools for developers working on the library.
• gui: Placeholder for future graphical user interface implementation.
• integrations: Placeholder for integration with other languages and domain-specific libraries.
• cases.py: Practical cases demonstrating the library’s functionality.
• configurations.py: Global parameters for the library’s behavior.
• custom_warnings.py: Custom warnings designed to help users with library-specific issues.

Example Projects

Here are a few example projects you can explore with the Ergodicity Library:

1. Simulating Financial Models: Apply the library’s tools to simulate and analyze geometric Brownian motion and other stochastic processes in financial markets.
2. Biological Population Dynamics: Use stochastic population models to simulate growth patterns in ecosystems and analyze stability using ergodic theory.
3. Training Artificial Agents: Implement machine learning agents that optimize their decision-making strategies under stochastic environments using evolutionary algorithms.

Contributions

The library is in active development, and contributions are welcome. Here’s how you can help:

1. Bug Reports & Feedback: If you encounter any bugs or have suggestions for improvements, feel free to report them on the GitHub issues page.
2. New Features & Modules: You can help by developing new features, improving existing ones, or expanding the library into new scientific domains like finance, biology, or physics.
3. Testing: If you are using the library for your own research, we would greatly appreciate your feedback and testing of its features.

To contribute, fork the repository and submit a pull request with your changes.

Roadmap

Future releases of the Ergodicity Library will include:

• Graphical User Interface (GUI): To enable easier interaction with the library without requiring deep programming knowledge.
• Expanded Machine Learning Support: Improved agent training models with integration of reinforcement learning and other neural network architectures.
• Performance Enhancements: Integration with C and Wolfram languages to optimize large-scale stochastic process simulations.
• New Domain-Specific Modules: Modules for domain-specific analysis in biology, finance, and physics.

License

The Ergodicity Library is open-source and licensed under the MIT License. See the LICENSE file for more details.