TY - BOOK ID - 213604 TI - A Basic Course in Probability Theory AU - Bhattacharya, Rabi. AU - Waymire, Edward C. PY - 2007 SN - 0387719393 0387719385 PB - New York, NY : Springer New York : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Probabilities. KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Math KW - Science KW - Distribution (Probability theory. KW - Global analysis (Mathematics). KW - Probability Theory and Stochastic Processes. KW - Measure and Integration. KW - Analysis. KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Measure theory. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Lebesgue measure KW - Measurable sets KW - Measure of a set KW - Algebraic topology KW - Integrals, Generalized KW - Measure algebras KW - Rings (Algebra) KW - 517.1 Mathematical analysis KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:213604 AB - The 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. ER -