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Discrete Stochastic Processes (MIT 6.262)

by Robert Gallager · MIT OpenCourseWare

Probabilistic systems evolving through random changes: Poisson processes, finite-state and countable Markov chains, renewal processes, random walks and martingales. 25 lecture videos, Gallager's open textbook, and problem sets and exams with solutions build the intuition to model systems in engineering, operations research and finance.

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MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

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An Intuitive Introduction to Probability

University of Zurich course taught by Karl Schmedders that builds probability from everyday examples: basic rules, conditional probability, applications, discrete random variables, and the normal distribution. Learners finish able to compute and interpret probabilities in practical decisions.

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Introduction to Stochastic Processes

A compact graduate-level textbook covering Markov chains in discrete and continuous time, optimal stopping, martingales, renewal processes, reversible chains, Brownian motion and stochastic integration. Readers learn to model random systems and compute hitting probabilities, stationary distributions and expected waiting times.

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Stochastic Processes

A classic graduate text built around problems and intuitive proofs, covering the Poisson process, renewal theory, Markov chains, martingales, random walks and Brownian motion. Readers learn to analyse queueing, reliability and other applied probability models using renewal and martingale arguments.

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