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.

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.