Reversible Markov Chains and Random Walks on Graphs
by David Aldous, James Allen Fill
Publisher: University of California, Berkeley 2014
Number of pages: 516
From the table of contents: General Markov Chains; Reversible Markov Chains; Hitting and Convergence Time, and Flow Rate, Parameters for Reversible Markov Chains; Special Graphs and Trees; Cover Times; Symmetric Graphs and Chains; Advanced L2 Techniques for Bounding Mixing Times; Some Graph Theory and Randomized Algorithms; Continuous State, Infinite State and Random Environment; Interacting Particles on Finite Graphs; Markov Chain Monte Carlo.
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by Alexander K. Hartmann - arXiv
This is a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous random variables.
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This is a draft textbook on data analysis methods, intended for a one-semester course for advance undergraduate students who have already taken classes in probability, mathematical statistics, and linear regression. It began as the lecture notes.
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Covered topics: stochastic integrals with respect to general semimartingales, stochastic differential equations based on these integrals, integration with respect to Poisson measures, stochastic differential equations for general Markov processes.
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