IPython Interactive Computing and Visualization Cookbook

Chapter 13. Stochastic Dynamical Systems

In this chapter, we will cover the following topics:

• Simulating a discrete-time Markov chain
• Simulating a Poisson process
• Simulating a Brownian motion
• Simulating a stochastic differential equation

Introduction

Stochastic dynamical systems are dynamical systems subjected to the effect of noise. The randomness brought by the noise takes into account the variability observed in real-world phenomena. For example, the evolution of a share price typically exhibits long-term behaviors along with faster, smaller-amplitude oscillations, reflecting day-to-day or hour-to-hour variations.

Applications of stochastic systems to data science include methods for statistical inference (such as Markov chain Monte Carlo) and stochastic ...