Introduction to Computational Stochastic PDEs, CUP (2014) publisher's website

This book gives a comprehensive introduction to numerical
methods and analysis of stochastic processes, random fields
and stochastic differential equations, and offers graduate
students and researchers powerful tools for understanding
uncertainty quantification for risk analysis. Coverage
includes traditional stochastic ODEs with white noise
forcing, strong and weak approximation, and the multi-level
Monte Carlo method. Later chapters apply the theory of random
fields to the numerical solution of elliptic PDEs with
correlated random data, discuss the Monte Carlo method, and
introduce stochastic Galerkin finite-element
methods. Finally, stochastic parabolic PDEs are
developed. Assuming little previous exposure to probability
and statistics, theory is developed in tandem with
state-of-the-art computational methods through worked
examples, exercises, theorems and proofs. The set of MATLAB
codes included (and downloadable) allows readers to perform
computations themselves and solve the test problems
discussed. Practical examples are drawn from finance,
mathematical biology, neuroscience, fluid flow modelling and
materials science.

Here's a list of typos and errors for the book.

This repository contains Python versions of most of the MATLAB code from the book (translated by T.Shardlow).

The original MATLAB codes are available in the MATLAB/ directory (organised by Chapter).

A translation into Julia is available here (thanks to J. Varela).