000 03579nam a22005295i 4500
001 978-0-387-71939-9
003 DE-He213
005 20160302162641.0
007 cr nn 008mamaa
008 100301s2007 xxu| s |||| 0|eng d
020 _a9780387719399
_9978-0-387-71939-9
024 7 _a10.1007/978-0-387-71939-9
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aBhattacharya, Rabi.
_eauthor.
245 1 2 _aA Basic Course in Probability Theory
_h[electronic resource] /
_cby Rabi Bhattacharya, Edward C. Waymire.
264 1 _aNew York, NY :
_bSpringer New York,
_c2007.
300 _aXII, 220 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext
505 0 _aRandom Maps, Distribution, and Mathematical Expectation -- Independence, Conditional Expectation -- Martingales and Stopping Times -- Classical Zero–One Laws, Laws of Large Numbers and Deviations -- Weak Convergence of Probability Measures -- Fourier Series, Fourier Transform, and Characteristic Functions -- Classical Central Limit Theorems -- Laplace Transforms and Tauberian Theorem -- Random Series of Independent Summands -- Kolmogorov's Extension Theorem and Brownian Motion -- Brownian Motion: The LIL and Some Fine-Scale Properties -- Skorokhod Embedding and Donsker's Invariance Principle -- A Historical Note on Brownian Motion.
520 _aThe book develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. With this goal in mind, the pace is lively, yet thorough. Basic notions of independence and conditional expectation are introduced relatively early on in the text, while conditional expectation is illustrated in detail in the context of martingales, Markov property and strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two highlights. The historic role of size-biasing is emphasized in the contexts of large deviations and in developments of Tauberian Theory. The authors assume a graduate level of maturity in mathematics, but otherwise the book will be suitable for students with varying levels of background in analysis and measure theory. In particular, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including the graduate textbook, Stochastic Processes with Applications.
650 0 _aMathematics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aMeasure theory.
650 0 _aProbabilities.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aMeasure and Integration.
650 2 4 _aAnalysis.
700 1 _aWaymire, Edward C.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387719382
830 0 _aUniversitext
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-71939-9
912 _aZDB-2-SMA
999 _c177953
_d177953