000			a
999			_c33083 _d33083
008			240320b xxu||||| |||| 00| 0 eng d
020			_a9783031142079
082			_a515.42 _bLEG
100			_aLe Gall, Jean-Francois
245			_aMeasure theory, probability, and stochastic processes
260			_bSpringer, _c2022 _aCham :
300			_axiv, 406 p. ; _bill., _c24 cm
365			_b49.99 _c€ _d93.50
490			_aGraduate texts in mathematics ; _vv295
504			_aIncludes bibliographical references and index.
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			_aMeasure and Integration
650			_aProbability Theory
650			_aStochastic Processes
942			_2ddc _cBK