Karhunen–Loève Approximation of Brownian Motion
Playing around with time series data in Observable, I decided to create a small interactive application to visualize the Karhunen-Loève (KL) approximation (Karhunen 1947) of Brownian motion. The widget at the end of this post lets you explore how KL works, illustrating how adding more terms in the series leads to increasingly accurate representations of Brownian paths. ...