Local martingale

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Related lectures (32)

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Martingales: Definitions and Theorems

Explores martingales, adaptability, and stopping times in stochastic processes.

Martingale Convergence Theorem

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

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.

Martingale Convergence Theorem: Proof and Stopping Time

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Martingales: Definitions and Properties

Explores the definitions and properties of martingales in probability theory, including key concepts and examples.

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