000 05975nam a22005295i 4500
001 978-0-387-35434-7
003 DE-He213
005 20250710083955.0
007 cr nn 008mamaa
008 100301s2006 xxu| s |||| 0|eng d
020 _a9780387354347
_a99780387354347
024 7 _a10.1007/978-0-387-35434-7
_2doi
082 0 4 _a519.2
_223
100 1 _aAthreya, Krishna B.
_eauthor.
245 1 0 _aMeasure Theory and Probability Theory
_h[recurso electrónico] /
_cby Krishna B. Athreya, Soumendra N. Lahiri.
264 1 _aNew York, NY :
_bSpringer New York,
_c2006.
300 _aXIII, 618 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Texts in Statistics,
_x1431-875X
505 0 _aMeasures and Integration: An Informal Introduction -- Measures -- Integration -- Lp-Spaces -- Differentiation -- Product Measures, Convolutions, and Transforms -- Probability Spaces -- Independence -- Laws of Large Numbers -- Convergence in Distribution -- Characteristic Functions -- Central Limit Theorems -- Conditional Expectation and Conditional Probability -- Discrete Parameter Martingales -- Markov Chains and MCMC -- Stochastic Processes -- Limit Theorems for Dependent Processes -- The Bootstrap -- Branching Processes.
520 _aThis is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute.
650 0 _aMATHEMATICS.
650 0 _aCOMPUTER SCIENCE.
650 0 _aOPERATIONS RESEARCH.
650 0 _aDISTRIBUTION (PROBABILITY THEORY).
650 0 _aMATHEMATICAL STATISTICS.
650 0 _aECONOMETRICS.
650 1 4 _aMATHEMATICS.
650 2 4 _aPROBABILITY THEORY AND STOCHASTIC PROCESSES.
650 2 4 _aMEASURE AND INTEGRATION.
650 2 4 _aSTATISTICAL THEORY AND METHODS.
650 2 4 _aOPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING.
650 2 4 _aPROBABILITY AND STATISTICS IN COMPUTER SCIENCE.
650 2 4 _aECONOMETRICS.
700 1 _aLahiri, Soumendra N.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387329031
830 0 _aSpringer Texts in Statistics,
_x1431-875X
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-35434-7
_zVer el texto completo en las instalaciones del CICY
912 _aZDB-2-SMA
942 _2ddc
_cER
999 _c57454
_d57454