A Basic Course in Probability Theory

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Beschreibung

Preface to Second Edition.- Preface to First Edition.- I. Random Maps, Distribution, and Mathematical Expectation.- II. Independence, Conditional Expectation.- III. Martingales and Stopping Times.- IV. Classical Central Limit Theorems.- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations.- VI. Fourier Series, Fourier Transform, and Characteristic Functions.- VII. Weak Convergence of Probability Measures on Metric Spaces.- VIII. Random Series of Independent Summands.- IX. Kolmogorov's Extension Theorem and Brownian Motion.- X. Brownian Motion: The LIL and Some Fine-Scale Properties.- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle.- XII. A Historical Note on Brownian Motion.- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium.- A. Measure and Integration.- B. Topology and Function Spaces.- C. Hilbert Spaces and Applications in Measure Theory.- References.- Symbol Index.- Subject Index.

Über den Autor

Rabi Bhattacharya is Professor of Mathematics at The University of Arizona. He is a Fellow of the Institute of Mathematical Statistics and a recipient of the U.S. Senior Scientist Humboldt Award and of a Guggenheim Fellowship. He has made significant contributions to the theory and application of Markov processes, and more recently, nonparametric statistical inference on manifolds. He has served on editorial boards of many international journals and has published several research monographs and graduate texts on probability and statistics.

Edward C. Waymire is Emeritus Professor of Mathematics at Oregon State University. He received a PhD in mathematics from the University of Arizona in the theory of interacting particle systems. His primary research concerns applications of probability and stochastic processes to problems of contemporary applied mathematics pertaining to various types of flows, dispersion, and random disorder. He is a former chief editor of the Annals of Applied Probability, and past president of the Bernoulli Society for Mathematical Statistics and Probability.

Both authors have co-authored numerous books, including A Basic Course in Probability Theory, which is an ideal companion to the current volume.

Zusammenfassung

Quicker paced introduction to the basics allows for a more in-depth treatment of such topics as convergence theory and Brownian motion

Self-contained and suitable for students with varying levels of background in analysis and measure theory

Includes a complete overview of basic measure theory and analysis (with proofs), and an extensive bibliography for further reading in the area

Written in a lively and engaging style

Second edition has additional exercises and expanded basic theory, and a new chapter on general Markov dependent sequences

Includes supplementary material: [...]

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2017
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xii 265 S.
ISBN-13:	9783319479729
ISBN-10:	3319479725
Sprache:	Englisch
Herstellernummer:	978-3-319-47972-9
Einband:	Kartoniert / Broschiert
Autor:	Bhattacharya, Rabi Waymire, Edward C.
Auflage:	2nd edition 2016
Hersteller:	Springer Palgrave Macmillan Springer International Publishing AG Universitext
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 16 mm
Von/Mit:	Rabi Bhattacharya (u. a.)
Erscheinungsdatum:	21.02.2017
Gewicht:	0,429 kg