000 02336nam a22002777a 4500
003 IIITD
005 20250429093051.0
008 250427b |||||||| |||| 00| 0 eng d
020 _a9783031142079
040 _aIIITD
082 _a515.42
_bLEG-M
100 _aLe Gall, Jean-Francois
245 _aMeasure theory, probability, and stochastic processes
_cby Jean-Francois Le Gall
260 _aSwitzerland :
_bSpringer,
_c©2022
300 _axiv, 406 p. ;
_c24 cm.
440 _aGraduate texts in mathematics
504 _aIncludes bibliographical references and index
505 _tPart 1 : Measure theory
505 _tPart 2 : Probability theory
505 _tPart 3 : Stochastic processes
520 _aThis textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis. Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illuminating exercises of varying difficulty. Some basic facts from functional analysis, in particular on Hilbert and Banach spaces, are included in the appendix. Measure Theory, Probability, and Stochastic Processes is an ideal text for readers seeking a thorough understanding of basic probability theory. Students interested in learning more about Brownian motion, and other continuous-time stochastic processes, may continue reading the authors more advanced textbook in the same series (GTM 274).
650 _aProbabilities
650 _aStochastic processes
650 _aMeasure theory
942 _cBK
_2ddc
999 _c189943
_d189943