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Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website. This book is intended for graduate students in engineering, mathematics, science, and statistics. Researchers who need to use probability theory will also find it useful. It is appropriate for graduate-level courses on measure theory and/or probability theory.
The volumes in this set, originally published between 1970 and 1996, draw together research by leading academics in the area of economic and financial markets, and provide a rigorous examination of related key issues. The volumes examine the stock exchange, capital cities as financial centres, international capital, the financial system, bond duration, security market indices and artificial intelligence applications on Wall Street, whilst also exploring the general principles and practices of financial markets in various countries. This set will be of particular interest to students of economics and finance respectively.
First published in 1982, Bond Duration and Immunization is a collection of seminal papers featuring articles from high profile academics such as Frederick McCaulay, John Hicks, and F.M. Redington. This collection also features several articles published in British actuarial journals often unavailable outside of the UK, and a strong collection of articles which contextually offer a significant contribution to the field. This strong collection will appeal to anyone working or researching in the area of bond duration and immunization.
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Selected by Choice magazine as an Outstanding Academic Title Jane Austen, arguably the most beloved of all English novelists, has been regarded both as a feminist ahead of her time and as a social conservative whose satiric comedies work to regulate rather than to liberate. Such viewpoints, however, do not take sufficient stock of the historical Austen, whose writings, as William Galperin shows, were more properly oppositional rather than either disciplinary or subversive. Reading the history of her novels' reception through other histories—literary, aesthetic, and social—The Historical Austen is a major reassessment of Jane Austen's achievement as well as a corrective to the historical Austen that abides in literary scholarship. In contrast to interpretations that stress the conservative aspects of the realistic tradition that Austen helped to codify, Galperin takes his lead from Austen's contemporaries, who were struck by her detailed attention to the dynamism of everyday life. Noting how the very act of reading demarcates an horizon of possibility at variance with the imperatives of plot and narrative authority, The Historical Austen sees Austen's development as operating in two registers. Although her writings appear to serve the interests of probability in representing "things as they are," they remain, as her contemporaries dubbed them, histories of the present, where reality and the prospect of change are continually intertwined. In a series of readings of the six completed novels, in addition to the epistolary Lady Susan and the uncompleted Sanditon, Galperin offers startling new interpretations of these texts, demonstrating the extraordinary awareness that Austen maintained not only with respect to her narrative practice—notably, free indirect discourse—but also with attention to the novel's function as a social and political instrument.