ILinOUProcess

This repository contains MATLAB scripts for simulating and analyzing Ornstein-Uhlenbeck (OU) stochastic processes, with a focus on investigating the relationship between Integral Linear Processes and Increment Covariances.

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📁 Repository Contents

File	Description
OUILvsIC.m	Script analyzing the relation between the OU process' integral linearity and increment covariances.
OUprocessSS.m	Computes steady-state properties of an Ornstein-Uhlenbeck process.
mainnoplot.m	Main script to run simulations without plotting. Useful for batch runs or data analysis.
ornstein_uhlenbeck_euler_maruyama.m	Implementation of the Euler-Maruyama method for simulating an Ornstein-Uhlenbeck process.
LICENSE	Project license file (MIT License).

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📚 Mathematical Background

The Ornstein-Uhlenbeck (OU) process is a classic stochastic process commonly used to model mean-reverting behaviors in physics, finance, and biology.

The project particularly investigates:

• Euler-Maruyama simulation of OU dynamics
• Steady-state statistics
• Integral linear properties versus incremental covariance

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🛠 Requirements

• MATLAB R2020b or newer
• (No special toolboxes required)

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🚀 How to Use

1. Clone the repository:

   git clone https://github.com/YOUR_USERNAME/ILinOUProcess.git

2. Add to MATLAB path:

   addpath(genpath('path_to_cloned_folder'))

3. Run a simulation, for example:

   run('OUILvsIC.m')

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✨ Highlights

• Simulate and visualize Ornstein-Uhlenbeck processes.
• Understand increment properties and covariance structures.
• Perform steady-state analysis of stochastic processes.

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📜 License

This project is licensed under the MIT License — see the LICENSE file for details.

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👨‍💻 Author

Developed by Adrian Guel.