Stochastic Processes & Brownian Motion

Memoryless processes on discrete state spaces: transition matrices, the Chapman-Kolmogorov equations, classification of

The simple random walk as the prototype process, its scaling toward Brownian motion, and the filtration formalism that m

The continuous-time limit of the random walk: its four defining axioms, existence, the Gaussian marginal structure, and

The single fact that makes stochastic calculus different: smooth paths have zero quadratic variation, but Brownian motio

Brownian motion as a Gaussian process, the multivariate normal toolkit, and how Radon-Nikodym densities and Girsanov&rsq