000			a
999			_c32360 _d32360
008			230829b xxu||||| |||| 00| 0 eng d
020			_a9783319479729
082			_a519.2 _bBHA
100			_aBhattacharya, Rabi
245			_aBasic course in probability theory
260			_bSpringer, _c2016 _aCham :
300			_axii, 265 p. ; _bill., _c24 cm
365			_b69.99 _cEUR _d94.90
490			_aUniversitext, _v0172-5939
504			_aIncludes bibliographical references and indexes.
520			_aThis text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, 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 a series of four upcoming graduate textbooks in stochastic processes with applications.
650			_aBanach space
650			_aConvergence
650			_aDistribution function
650			_aFatou's lemma
650			_aFourier inversion formula
650			_a Random variables
650			_a Stokes law
650			_aTruncation method
650			_aZero-one law
650			_aMarkov property
650			_aMartingales
650			_aStochastic processes
700			_aWaymire, Edward C.
942			_2ddc _cBK