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000931579 019__ $$a1153072817$$a1153320478
000931579 020__ $$a9783030401832$$q(electronic book)
000931579 020__ $$a3030401839$$q(electronic book)
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000931579 0247_ $$a10.1007/978-3-030-40183-2$$2doi
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000931579 035__ $$aSP(OCoLC)1151190653$$z(OCoLC)1153072817$$z(OCoLC)1153320478
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000931579 08204 $$a519.2$$223
000931579 1001_ $$aBrémaud, Pierre.
000931579 24510 $$aProbability theory and stochastic processes /$$cPierre Brémaud.
000931579 260__ $$aCham :$$bSpringer,$$c2020.
000931579 300__ $$a1 online resource (717 pages).
000931579 336__ $$atext$$btxt$$2rdacontent
000931579 337__ $$acomputer$$bc$$2rdamedia
000931579 338__ $$aonline resource$$bcr$$2rdacarrier
000931579 347__ $$atext file$$bPDF$$2rda
000931579 4901_ $$aUniversitext
000931579 504__ $$aIncludes bibliographical references and index.
000931579 5050_ $$aIntroduction.-Warming Up -- Integration Theory for Probability -- Probability and Expectation -- Convergence of random sequences -- Markov Chains -- Martingale Sequences -- Ergodic Sequences -- Generalities on Stochastic Processes -- Poisson Processes -- Continuous-Time Markov Chains -- Renewal Theory in Continuous Time -- Brownian Motion -- Wide-sense Stationary Stochastic Processes -- An Introduction to Itô's Calculus -- Appenndix: Number Theory and Linear Algebra -- Analysis -- Hilbert Spaces -- Z-Transforms -- Proof of Paul Lévy's Criterion -- Direct Riemann Integrability -- Bibliography -- Index. 
000931579 506__ $$aAccess limited to authorized users.
000931579 520__ $$aThe ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.
000931579 588__ $$aDescription based on print version record.
000931579 650_0 $$aProbabilities.
000931579 77608 $$iPrint version:$$aBrémaud, Pierre$$tProbability Theory and Stochastic Processes$$dCham : Springer International Publishing AG,c2020$$z9783030401825
000931579 830_0 $$aUniversitext.
000931579 852__ $$bebk
000931579 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-40183-2$$zOnline Access$$91397441.1
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