sde: a simple tool for numerical stochastic differential equations

sde provides basic tools for simulating brownian motions which is the basic ingredients to lots of SDE models, performing different types of stochastic integrations, Eular-Maruyama methods and so much more (to come…).

The origin of this project is this wonderful introductory paper: by Desmond J. Higham.

In this document, we will demonstrate how to:

• Simulate brownian motion paths

• Transform simulated bm paths

• Perform stochastic integrals

• Carry out numerical sde methods

However, before we get started, we need to install the package first which is freely available on PyPI.

Dependencies

Dependencies

Package	Version
python	>=3.9
numpy	==1.24.2
tqdm	==4.64.1
matplotlib	==3.7.1

Installation

Note

We highly recommend creating a virtual environment before proceeding to installing the package. For how to manage virtual environment via conda, check out their tutorial.

pip install sdeIU

To quickly test if it has been installed:

python -m sde --version

Tutorial

Brownian Motions

• The basic ingredients: Brownian Motions
  • Generate Brownian Paths
  • Transform Brownian Paths

Stochastic Integrals

• Stochastic Integrals
  • Ito Integrals
  • Stratonovich Integrals

Stochastic Differential Equations

• Stochastic Differential Equations
  • The Euler-Maruyama Method
  • Milstein’s Higher Order Method
  • Stochastic Chain Rule

Convergence and Stability

• Convergence and Stability
  • Strong Convergence
  • Weak Convergence
  • Linear Stability

API Reference

• API Reference

Indices and tables

• Index

• Module Index

• Search Page