LEADER 06013nam 22007335 450 001 9910299974503321 005 20200703084635.0 010 $a0-8176-8409-3 024 7 $a10.1007/978-0-8176-8409-9 035 $a(CKB)3710000000078521 035 $a(Springer)9780817684099 035 $a(MH)013879477-4 035 $a(DE-He213)978-0-8176-8409-9 035 $a(MiAaPQ)EBC3091961 035 $a(PPN)176095500 035 $a(EXLCZ)993710000000078521 100 $a20131113d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Probability Path /$fby Sidney I. Resnick 205 $a1st ed. 2014. 210 1$aBoston, MA :$cBirkhäuser Boston :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XIV, 453 p. 11 illus.)$conline resource 225 1 $aModern Birkhäuser Classics,$x2197-1803 300 $aOriginally published 1999, reprint of 5th printing. 300 $aReprint of the 2005 edition. 311 $a0-8176-8408-5 320 $aIncludes bibliographical references and index. 327 $aSets and events -- Probability spaces -- Random variables, elements, and measurable maps -- Independence -- Integration and expectation -- Convergence concepts -- Laws of large numbers and sums of independent random variables -- Convergence in distribution -- Characteristic functions and the central limit theorem -- Martingales. 330 $aMany probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.   A one-semester course is laid out in an efficient and readable manner covering the core material. The first three chapters provide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applications to statistics (quantile and distribution function estimation), and applied probability. Two subsequent chapters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treats conditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance.   Like Adventures in Stochastic Processes, Resnick?s related and very successful textbook, A Probability Path is rich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprint is designed to make this classic textbook available to a wider audience.                                                             This book is different from the classical textbooks on probability theory in that it treats the measure theoretic background not as a prerequisite but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand the deeper concepts of current day advanced probability as it is used in statistics, engineering, biology and finance.... The pace of the book is quick and disciplined. Yet there are ample examples sprinkled over the entire book and each chapter finishes with a wealthy section of inspiring problems. ?Publications of the International Statistical Institute       This textbook offers material for a one-semester course in probability, addressed to students whose primary focus is not necessarily mathematics.... Each chapter is completed by an exercises section. Carefully selected examples enlighten the reader in many situations. The book is an excellent introduction to probability and its applications. ?Revue Roumaine de Mathématiques Pures et Appliquées. 410 0$aModern Birkhäuser Classics,$x2197-1803 606 $aProbabilities 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aOperations research 606 $aManagement science 606 $aStatistics  606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aOperations Research, Management Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M26024 606 $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001 615 0$aProbabilities. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aOperations research. 615 0$aManagement science. 615 0$aStatistics . 615 14$aProbability Theory and Stochastic Processes. 615 24$aApplications of Mathematics. 615 24$aOperations Research, Management Science. 615 24$aStatistical Theory and Methods. 676 $a519.2 700 $aResnick$b Sidney I$4aut$4http://id.loc.gov/vocabulary/relators/aut$0103650 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299974503321 996 $aProbability path$91410553 997 $aUNINA 999 $aThis 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