I’ll discuss the use of operator splitting as the basis for numerically solving ODEs or PDEs with some concrete examples. Along the way, we’ll stumble into a lot of linear algebra and a teensy bit of Lie theory.

I’ll discuss the use of operator splitting as the basis for numerically solving ODEs or PDEs with some concrete examples. Along the way, we’ll stumble into a lot of linear algebra and a teensy bit of Lie theory.

In this post, I’ll discuss some recent explanations for anomalous, yet Gaussian diffusion, including diffusing diffusivities and stochastic subordination.

In the previous post about limit theorems of stochastic processes, we considered when everything goes *right*, leading to Gaussian-like behavior. Here we’ll discuss when things go *wrong*, particularly when memory effects and infinite moments are introduced.

A few months ago, Frank Stenger uploaded a preprint of a proposed proof of the Riemann hypothesis. Unlike the plethora of other attempts at famous problems, nobody seems to be talking about this. *Why?*

One way to understand the structure of randomness is to experience *a lot* of it. We’ll use $\lim_{n\to\infty} X_1 + \cdots + X_n$ as a case study, and along the way bump into classical ideas like the Central Limit Theorem (CLT) and Brownian motion.