05857nam 22008895 450 991029997440332120200705161932.01-4471-5361-810.1007/978-1-4471-5361-0(CKB)3710000000078526(Springer)9781447153610(MH)013879479-0(SSID)ssj0000988251(PQKBManifestationID)11583334(PQKBTitleCode)TC0000988251(PQKBWorkID)10952215(PQKB)11038098(DE-He213)978-1-4471-5361-0(MiAaPQ)EBC6315095(MiAaPQ)EBC1394842(Au-PeEL)EBL1394842(CaPaEBR)ebr10983438(OCoLC)870244268(PPN)172418097(EXLCZ)99371000000007852620130829d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierProbability Theory A Comprehensive Course /by Achim Klenke2nd ed. 2014.London :Springer London :Imprint: Springer,2014.1 online resource (XII, 638 p. 46 illus., 20 illus. in color.)online resourceUniversitext,0172-5939Bibliographic Level Mode of Issuance: Monograph1-4471-5360-X Basic Measure Theory -- Independence -- Generating Functions -- The Integral -- Moments and Laws of Large Numbers -- Convergence Theorems -- Lp-Spaces and the Radon–Nikodym Theorem -- Conditional Expectations -- Martingales -- Optional Sampling Theorems -- Martingale Convergence Theorems and Their Applications -- Backwards Martingales and Exchangeability -- Convergence of Measures -- Probability Measures on Product Spaces -- Characteristic Functions and the Central Limit Theorem -- Infinitely Divisible Distributions -- Markov Chains -- Convergence of Markov Chains -- Markov Chains and Electrical Networks -- Ergodic Theory -- Brownian Motion -- Law of the Iterated Logarithm -- Large Deviations -- The Poisson Point Process -- The Itˆo Integral -- Stochastic Differential Equations.This second edition of the popular textbook contains a comprehensive course in modern probability theory. Overall, probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us in understanding magnetism, amorphous media, genetic diversity and the perils of random developments at financial markets, and they guide us in constructing more efficient algorithms. To address these concepts, the title covers a wide variety of topics, many of which are not usually found in introductory textbooks, such as: • limit theorems for sums of random variables • martingales • percolation • Markov chains and electrical networks • construction of stochastic processes • Poisson point process and infinite divisibility • large deviation principles and statistical physics • Brownian motion • stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.Universitext,0172-5939ProbabilitiesMeasure theoryDynamicsErgodic theoryFunctional analysisStatistical physicsDynamicsProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Probabilities.Measure theory.Dynamics.Ergodic theory.Functional analysis.Statistical physics.Dynamics.Probability Theory and Stochastic Processes.Measure and Integration.Dynamical Systems and Ergodic Theory.Functional Analysis.Complex Systems.Statistical Physics and Dynamical Systems.519.2Klenke Achimauthttp://id.loc.gov/vocabulary/relators/aut478404MiAaPQMiAaPQMiAaPQBOOK9910299974403321Probability theory264282UNINAThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress