Martingales and Brownian Motion

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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.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

Martingales and Brownian Motion: Drift and Exit Time

Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.