some math!
(this page is under construction and most notes are incomplete)
Summaries, thoughts, and comments on Prof. Andrew Gelman’s Bayesian Data Analysis (3rd ed.)
The Riemann-Stieltjes integral generalizes the Riemann integral, allowing us to integrate functions (an integrand) with respect to other functions (the integrator). In stochastic integration, we’d like to consider a random integrator. We can imagine this as integrating a function weighted randomly, rather than by interval width (Riemann) or a deterministic function (Riemann-Stieltjes). Is this possible? There are a couple of bumps in the road…
A first undergraduate course in stochastic processes will simply assert the existence of Brownian motion and its properties. Let’s pretend it’s 1900 and prove existence of Brownian Motion via Kolmogorov and Lévy constructions.
Notes and reference for some intro crypt + zero knowledge. IN PROGRESS.
Notes and relevant papers / readings for geometric and topological methods in machine learning. IN PROGRESS.
Trying to write a non-rigorous Brownian motion cheatsheet, failing, and giving up…
Scattered notes from Prof. Joe Chang’s stochastic processes book, intended for a first undergraduate course. Brownian motion and stochastic integration largely omitted; some sections left incomplete and proofs largely reference the book. See other posts for more details on stochastic calculus.