Martingales and Brownian Motion: Construction and Properties

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Girsanov: Martingales and Brownian Motion

Explores martingales, Brownian motion, and measure transformations in probability theory.

White Noise Form of the Langevin Equation

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

Martingale Convergence Theorem

Explains the martingale convergence theorem and its applications in probability theory.

Stochastic Calculus: Integrals and Processes

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

Stochastic Processes: Brownian Motion

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

Martingales and Brownian Motion: Three Stopping Theorems

Explores three stopping theorems in martingales and Brownian motion.

Brownian Motion: Molecular Nature Revealed

Explores the history, mathematical models, and experimental techniques of Brownian Motion, revealing its molecular nature and significance in cell biology.

Fourier Transform and Spectral Densities

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

Martingales and Brownian Motion

Discusses the construction of random variables similar to Brownian motion and their implications.

Martingale Convergence Theorem: Version 1

Introduces the martingale convergence theorem and demonstrates its application with examples.