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001450960 001__ 1450960
001450960 003__ OCoLC
001450960 005__ 20230310004636.0
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001450960 008__ 221104s2022\\\\sz\\\\\\ob\\\\001\0\eng\d
001450960 020__ $$a9783031142055$$q(electronic bk.)
001450960 020__ $$a3031142055$$q(electronic bk.)
001450960 020__ $$z3031142047
001450960 020__ $$z9783031142048
001450960 0247_ $$a10.1007/978-3-031-14205-5$$2doi
001450960 035__ $$aSP(OCoLC)1350250998
001450960 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dOCLCF$$dEMK$$dUKAHL$$dOCLCQ
001450960 049__ $$aISEA
001450960 050_4 $$aQA312
001450960 08204 $$a515/.42$$223/eng/20221104
001450960 1001_ $$aLe Gall, J. F.$$q(Jean-François),$$eauthor.
001450960 24510 $$aMeasure theory, probability, and stochastic processes /$$cJean-François Le Gall.
001450960 264_1 $$aCham, Switzerland :$$bSpringer,$$c2022.
001450960 300__ $$a1 online resource :$$billustrations (black and white, and color).
001450960 336__ $$atext$$btxt$$2rdacontent
001450960 337__ $$acomputer$$bc$$2rdamedia
001450960 338__ $$aonline resource$$bcr$$2rdacarrier
001450960 4901_ $$aGraduate texts in mathematics ;$$v295
001450960 504__ $$aIncludes bibliographical references and index.
001450960 5050_ $$aPart I. Measure Theory -- Chapter 1. Measurable Spaces -- Chapter 2. Integration of Measurable Functions -- Chapter 3. Construction of Measures -- Chapter 4. Lp Spaces -- Chapter 5. Product Measure -- Chapter 6. Signed Measures -- Chapter 7. Change of Variables -- Part II. Probability Theory -- Chapter 8. Foundations of Probability Theory -- Chapter 9. Independence -- Chapter 10. Convergence of Random Variables -- Chapter 11. Conditioning -- Part III. Stochastic Processes -- Chapter 12. Theory of Martingales -- Chapter 13. Markov Chains -- Chapter 14. Brownian Motion.
001450960 506__ $$aAccess limited to authorized users.
001450960 520__ $$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).
001450960 588__ $$aDescription based on print version record.
001450960 650_0 $$aMeasure theory.
001450960 650_0 $$aProbabilities.
001450960 650_0 $$aStochastic processes.
001450960 655_0 $$aElectronic books.
001450960 77608 $$iPrint version:$$aLE GALL, JEAN-FRANCOIS.$$tMEASURE THEORY, PROBABILITY, AND STOCHASTIC PROCESSES.$$d[Place of publication not identified] : SPRINGER INTERNATIONAL PU, 2022$$z3031142047$$w(OCoLC)1334883217
001450960 830_0 $$aGraduate texts in mathematics ;$$v295.
001450960 852__ $$bebk
001450960 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-14205-5$$zOnline Access$$91397441.1
001450960 909CO $$ooai:library.usi.edu:1450960$$pGLOBAL_SET
001450960 980__ $$aBIB
001450960 980__ $$aEBOOK
001450960 982__ $$aEbook
001450960 983__ $$aOnline
001450960 994__ $$a92$$bISE