02394cam a2200301 a 450000100090000000300020000900500170001100800410002801000170006902000290008602000250011504000180014004200080015805000220016610000230018824500650021125000120027626000640028830000260035250400510037850400510042952013530048065000190183390600450185294200120189799900170190995201660192616307420O20140923131113.0100628s2011    nyu      b    001 0 eng    a  2010027652  a9780521761581 (hardback)  a9780521132503 (pbk.)  aPULcPULdPUL  apcc00aQA273b.S763 20111 aStroock, Daniel W.10aProbability theory :ban analytic view /cDaniel W. Stroock.  a2nd ed.  aCambridge ;aNew York :bCambridge University Press,c2011.  axxi, 527 p. ;c27 cm.  aIncludes bibliographical references and index.  aIncludes bibliographical references and index.  a"This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It is intended to provide readers with an introduction to probability theory and the analytic ideas and tools on which the modern theory relies. It includes more than 750 exercises. Much of the content has undergone significant revision. In particular, the treatment of Levy processes has been rewritten, and a detailed account of Gaussian measures on a Banach space is given. The first part of the book deals with independent random variables, Central Limit phenomena, and the construction of Levy processes, including Brownian motion. Conditioning is developed and applied to discrete parameter martingales in Chapter 5, Chapter 6 contains the ergodic theorem and Burkholder's inequality, and continuous parameter martingales are discussed in Chapter 7. Chapter 8 is devoted to Gaussian measures on a Banach space, where they are treated from the abstract Wiener space perspective. The abstract theory of weak convergence is developed in Chapter 9, which ends with a proof of Donsker's Invariance Principle. The concluding two chapters contain applications of Brownian motion to the analysis of partial differential equations and potential theory"-- 0aProbabilities.  a7bcbccorignewd1eecipf20gy-gencatlg  2lcccBK  c24094d24094  00102lcc40708NFICaPUEAbPUEAcGENd2014-09-23eBook for Africag5000.00l1oQA273 .S763 2011p2014-1862r2020-02-21 00:00:00s2019-12-11tC1w2014-09-23yBK