chapter13_stochastic.md

13. Stochastic Dynamical Systems

Full list of references in Chapter 13 of the IPython Cookbook, the definitive guide to high-performance scientific computing and data science in Python, by Dr. Cyrille Rossant, Packt Publishing, 400 pages, 2014.

Recipe 1

• Markov chains,
• Absorbing Markov chains,
• Monte-Carlo methods.

Recipe 2

• Poisson process,
• Point process,
• Continuous-time process,
• Renewal processes.

Recipe 3

Recipe 4

• Stochastic differential equations.
• The white noise, derivative of the Brownian motion.
• The Langevin equation.
• The Ornstein-Uhlenbeck process is solution of the Langevin equation.
• Diffusion processes (generalization of the Ornstein-Uhlenbeck process).
• Itô calculus generalizes differential calculus to stochastic processes.
• The Euler-Maruyama method is a simple numerical method for simulating diffusion processes.