Martingales and Brownian Motion

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Martingales and Brownian Motion: Convergence Criteria and Theorems

Explores convergence criteria for martingales, including almost sure convergence and Cauchy criterion, leading to the first martingale convergence theorem.