Modern Discrete Probability: An Essential Toolkit (Cambridge Series in Statistical and Probabilistic Mathematics) (1版)

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【簡介】 Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering. 【目錄】

MODERN STATISTICAL,SYSTEMS AND GPSS SIMULATION

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Modern Statistical, Systems, and GPSS Simulation, Second Edition introduces the theory and implementation of discrete-event simulation. This text: establishes a theoretical basis for simulation methodology provides details of an important simulation language (GPSS - General Purpose Simulation System) integrates these two elements in a systems simulation case study Valuable additions to the second edition include coverage of random number generators with astronomic period, new entropy-based tests of uniformity, gamma variate generation, results on the GLD, and variance reduction techniques. GPSS/PC is an interactive implementation of GPSS for the IBM-PC compatible family of microcomputers. The disk accompanying Modern Statistical, Systems, and GPSS Simulation contains the limited educational version of GPSS/PC with many illustrative examples discussed in the text.