Le Gall

Measure Theory, Probability, and Stochastic Processes

Springer

ISBN 978-3-031-14207-9

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Bibliografische Daten

Fachbuch

Buch. Softcover

2023

5 s/w-Abbildungen, 1 Farbabbildung, Bibliographien.

In englischer Sprache

Umfang: xiv, 406 S.

Format (B x L): 15,5 x 23,5 cm

Gewicht: 755

Verlag: Springer

ISBN: 978-3-031-14207-9

Weiterführende bibliografische Daten

Das Werk ist Teil der Reihe: Graduate Texts in Mathematics; 295

Produktbeschreibung

This 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 author’s more advanced textbook in the same series (GTM 274).

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Kundeninformationen

Provides a rigorous treatment of measure theory geared towards the general theory of stochastic processes Highlights the interplay between probability and other areas of mathematics such as complex variables or PDE's Appeals to mathematicians and scientists in need of a thorough knowledge of probability theory

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