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Frederick Mosteller has inspired numerous statisticians and other scientists by his creative approach to statistics and its applications. This volume brings together 40 of his most original and influential papers, capturing the variety and depth of his writings. The editors hope to share these with a new generation of researchers, so that they can build upon his insights and efforts. This volume of selected papers is a companion to the earlier volume A Statistical Model: Frederick Mosteller's Contributions to Statistics, Science, and Public Policy, edited by Stephen E. Fienberg, David C. Hoaglin, William H. Kruskal, and Judith M. Tanur (Springer-Verlag, 1990), and to Mosteller's forthcoming autobiography, which will also be published by Springer-Verlag. It includes a biography and a comprehensive bibliography of Mosteller's books, papers, and other writings. Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science, in the Departments of Statistics and Machine Learning at Carnegie Mellon University, Pittsburgh, PA. David C. Hoaglin is Principal Scientist at Abt Associates Inc., Cambridge, MA.

Mathematical statistics. --- Mathematics. --- Math --- Science --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Distribution (Probability theory. --- Educational tests and measuremen. --- Statistics. --- Econometrics. --- Probability Theory and Stochastic Processes. --- Public Health. --- Assessment, Testing and Evaluation. --- Statistical Theory and Methods. --- Statistics for Social Sciences, Humanities, Law. --- Economics, Mathematical --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Mathematical statistics

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The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background. The Ito calculus was originally motivated by the construction of Markov diffusion processes from infinitesimal generators. Previously, the construction of such processes required several steps, whereas Ito constructed these diffusion processes directly in a single step as the solutions of stochastic integral equations associated with the infinitesimal generators. Moreover, the properties of these diffusion processes can be derived from the stochastic integral equations and the Ito formula. This introductory textbook on stochastic integration provides a concise introduction to the Ito calculus, and covers the following topics: * Constructions of Brownian motion; * Stochastic integrals for Brownian motion and martingales; * The Ito formula; * Multiple Wiener-Ito integrals; * Stochastic differential equations; * Applications to finance, filtering theory, and electric circuits. The reader should have a background in advanced calculus and elementary probability theory, as well as a basic knowledge of measure theory and Hilbert spaces. Each chapter ends with a variety of exercises designed to help the reader further understand the material. Hui-Hsiung Kuo is the Nicholson Professor of Mathematics at Louisiana State University. He has delivered lectures on stochastic integration at Louisiana State University, Cheng Kung University, Meijo University, and University of Rome "Tor Vergata," among others. He is also the author of Gaussian Measures in Banach Spaces (Springer 1975), and White Noise Distribution Theory (CRC Press 1996), and a memoir of his childhood growing up in Taiwan, An Arrow Shot into the Sun (Abridge Books 2004).

Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Econometrics --- Math --- Science --- Methodology --- Stochastic integrals. --- Martingales (Mathematics) --- Stochastic processes --- Integrals, Stochastic --- Stochastic analysis --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical .

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There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference[248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s,p wards (white noise case). The Sobolev spaces D , with s is an arbitrary real number, are introduced following Watanabe’s work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe’s ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented.

Malliavin calculus. --- Stochastic analysis. --- Calculus, Malliavin --- Stochastic analysis --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Distribution (Probability theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Calculus of variations. --- Malliavin, Calcul de. --- Calcul des variations.

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Dedicated to the eminent Russian mathematician Albert Shiryaev on the occasion of his 70th birthday, the Festschrift is a collection of papers, including several surveys, written by his former students, co-authors and colleagues. These reflect the wide range of scientific interests of the teacher and his Moscow school. The topics range from the disorder problems to stochastic calculus and their applications to mathematical economics and finance. A full biobibliography of Shiryaev’s works is included. The book represents the modern state of art of many aspects of a quickly maturing theory and will be an essential source and reading for researchers in this area. The diversity of the topics and the comprehensive style of the papers make the book amenable and attractive for PhD students and young researchers.

Stochastic analysis --- Business mathematics --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- Distribution (Probability theory. --- System theory. --- Probability Theory and Stochastic Processes. --- Systems Theory, Control. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Systems theory. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Proofs from THE BOOK è un'opera straordinaria che ha saputo calamitare l'interesse di numerosissimi lettori, matematici e non, come poche altre di argomento matematico apparse in questi ultimi anni. Dall'edizione originale in lingua inglese, pubblicata nel 1998, sono poi state prodotte due altre edizioni in inglese e un numero in continua crescita di traduzioni in altre lingue (undici alla data in cui diamo alle stampe questa edizione). Proofs from THE BOOK rappresenta un'opera unica nel suo genere. La matematica è una disciplina costruita su teorie codificate in lemmi e teoremi le cui dimostrazioni sono sempre rigorose, spesso avvincenti e creative, talvolta bellissime. E' proprio la tensione dei matematici di ogni epoca, che li spinge a cercare dimostrazioni belle, ad aver ispirato gli autori, i quali, insieme con il grande matematico ungherese Paul Erdos, immaginano che vi sia UN LIBRO (forse addirittura di ispirazione divina) che contenga le dimostrazioni più significative ed avvincenti della matematica, quelle che rasentano la perfezione. E questa monografia vuole proporre alcuni esempi di dimostrazioni che, presumibilmente, dovrebbero trovare posto nel LIBRO, cioè in THE BOOK.

Mathematics. --- Geometry. --- Mathematics --- Euclid's Elements --- Math --- Science --- Algebra. --- Combinatorics. --- Number theory. --- Distribution (Probability theory. --- Mathematics, general. --- Number Theory. --- Probability Theory and Stochastic Processes. --- Number study --- Numbers, Theory of --- Algebra --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical analysis --- Combinatorics --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk