Girsanov: Martingales and Brownian Motion

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Page 3 of 4

Explores martingales, Brownian motion, submartingales, descents monitoring, and convergence theorems with practical examples.

Martingale Convergence Theorem: Version 1

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

Optional Stopping Theorem: Martingales and Stepping Times

Explores the optional stopping theorem for martingales and stepping times, emphasizing its applications and implications.

Martingales and Brownian Motion: Drift and Exit Time

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

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Martingales and Brownian Motion

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Fourier Transform and Spectral Densities

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

Martingales and Brownian Motion: Construction and Properties

Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.

Martingales and Brownian Motion

Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.

Semimartingale: Joint Variation Process

Covers semimartingales, Ito's lemma, and polynomial demonstrations, emphasizing the management of second-order terms and induction reasoning.