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Doob's martingale convergence theorems
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Related lectures (32)
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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 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.
Quadratic Variation: Martingales and Stochastic Integrals
Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.
Martingale Convergence Theorem
Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.
Martingales and Brownian Motion: Drift and Exit Time
Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.
Martingale Theory: Basics and Applications
Covers the basics of Martingale theory and its applications in random variables.
Martingales: Definitions and Properties
Explores the definitions and properties of martingales in probability theory, including key concepts and examples.
Generalization of Martingales
Explores the generalization of Martingale Central Limit Theorem to sub- and supermartingales, discussing key properties and corollaries.
Reflection Principle: Proof and Observations
Covers the reflection principle and martingale writing in simple symmetric random walks.
Risk Minimization from Adaptively Collected Data
Explores risk minimization from adaptively collected data with guarantees for policy learning and the importance of exploration strategies.
Stochastic Integral: Isometry Continuity
Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.
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