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020 _a9781447152019
_9978-1-4471-5201-9
024 7 _a10.1007/978-1-4471-5201-9
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aBorovkov, Alexandr A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aProbability Theory
_h[electronic resource] /
_cby Alexandr A. Borovkov.
250 _a1st ed. 2013.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2013.
300 _aXXVIII, 733 p. 22 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aDiscrete Spaces of Elementary Events -- An Arbitrary Space of Elementary Events -- Random Variables and Distribution Functions -- Numerical Characteristics of Random Variables -- Sequences of Independent Trials with Two Outcomes -- On Convergence of Random Variables and Distributions -- Characteristic Functions -- Sequences of Independent Random Variables. Limit Theorems -- Large Deviation Probabilities for Sums of Independent Random Variables -- Renewal Processes -- Properties of the Trajectories of Random Walks. Zero-One Laws -- Random Walks and Factorisation Identities -- Sequences of Dependent Trials. Markov Chains -- Information and Entropy -- Martingales -- Stationary Sequences -- Stochastic Recursive Sequences -- Continuous Time Random Processes -- Processes with Independent Increments -- Functional Limit Theorems -- Markov Processes -- Processes with Finite Second Moments. Gaussian Processes -- Appendices.
520 _aProbability theory is an actively developing branch of mathematics. It has applications in many areas of science and technology and forms the basis of mathematical statistics. This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent. The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful and esteemed Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and makes it an invaluable source of reference for Western researchers and advanced students in probability related subjects. Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study. About the Author Professor Alexandr Borovkov lives and works in the Novosibirsk Academy Town in Russia and is affiliated with both the Sobolev Institute of Mathematics of the Russian Academy of Sciences and the Novosibirsk State University. He is one of the most prominent Russian specialists in probability theory and mathematical statistics. Alexandr Borovkov authored and co-authored more than 200 research papers and ten research monographs and advanced level university textbooks. His contributions to mathematics and its applications are widely recognized, which included election to the Russian Academy of Sciences and several prestigious awards for his research and textbooks.
650 0 _aProbabilities.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447152026
776 0 8 _iPrinted edition:
_z9781447152002
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttps://doi.org/10.1007/978-1-4471-5201-9
912 _aZDB-2-SMA
999 _c17978
_d17978
942 _cebook