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008			150903s2006 xxu| o |||| 0|eng d
020			_a9780387354347 _99780387354347
024	7		_a10.1007/9780387354347 _2doi
035			_avtls000331247
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050		4	_aQA273.A1-274.9
100	1		_aAthreya, Krishna B. _eautor _9301631
245	1	0	_aMeasure Theory and Probability Theory / _cby Krishna B. Athreya, Soumendra N. Lahiri.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_axiii, 618 páginas, _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aSpringer Texts in Statistics, _x1431-875X
500			_aSpringer eBooks
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.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aLahiri, Soumendra N. _eautor _9301632
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9780387329031
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-387-35434-7 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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