The Splendors And Miseries Of Martingales

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The Splendors and Miseries of Martingales

Laurent Mazliak,Glenn Shafer
The Splendors and Miseries of Martingales Book PDF

Author : Laurent Mazliak,Glenn Shafer
Publisher : Springer Nature
Page : 419 pages
File Size : 54,9 Mb
Release : 2022-10-17
Category : Mathematics
ISBN : 9783031059889

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The Splendors and Miseries of Martingales by Laurent Mazliak,Glenn Shafer Pdf

Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler’s holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.

Mathematical Communities in the Reconstruction After the Great War 1918–1928

Laurent Mazliak,Rossana Tazzioli
Mathematical Communities in the Reconstruction After the Great War 1918 1928 Book PDF

Author : Laurent Mazliak,Rossana Tazzioli
Publisher : Springer Nature
Page : 373 pages
File Size : 40,7 Mb
Release : 2021-03-27
Category : Science
ISBN : 9783030616830

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Mathematical Communities in the Reconstruction After the Great War 1918–1928 by Laurent Mazliak,Rossana Tazzioli Pdf

This book is a consequence of the international meeting organized in Marseilles in November 2018 devoted to the aftermath of the Great War for mathematical communities. It features selected original research presented at the meeting offering a new perspective on a period, the 1920s, not extensively considered by historiography. After 1918, new countries were created, and borders of several others were modified. Territories were annexed while some countries lost entire regions. These territorial changes bear witness to the massive and varied upheavals with which European societies were confronted in the aftermath of the Great War. The reconfiguration of political Europe was accompanied by new alliances and a redistribution of trade – commercial, intellectual, artistic, military, and so on – which largely shaped international life during the interwar period. These changes also had an enormous impact on scientific life, not only in practice, but also in its organization and communication strategies. The mathematical sciences, which from the late 19th century to the 1920s experienced a deep disciplinary evolution, were thus facing a double movement, internal and external, which led to a sustainable restructuring of research and teaching. Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. This was accompanied by an explosion of new international or national associations of mathematicians with for instance the founding, in 1918, of the International Mathematical Union and the controversial creation of the International Research Council. Therefore, the central idea for the articulation of the various chapters of the book is to present case studies illustrating how in the aftermath of the war, many mathematicians had to organize their personal trajectories taking into account the evolution of the political, social and scientific environment which had taken place at the end of the conflict.

Applied Time Series Analysis

Terence C. Mills
Applied Time Series Analysis Book PDF

Author : Terence C. Mills
Publisher : Academic Press
Page : 354 pages
File Size : 45,8 Mb
Release : 2019-01-22
Category : Business & Economics
ISBN : 9780128131183

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Applied Time Series Analysis by Terence C. Mills Pdf

Written for those who need an introduction, Applied Time Series Analysis reviews applications of the popular econometric analysis technique across disciplines. Carefully balancing accessibility with rigor, it spans economics, finance, economic history, climatology, meteorology, and public health. Terence Mills provides a practical, step-by-step approach that emphasizes core theories and results without becoming bogged down by excessive technical details. Including univariate and multivariate techniques, Applied Time Series Analysis provides data sets and program files that support a broad range of multidisciplinary applications, distinguishing this book from others. Focuses on practical application of time series analysis, using step-by-step techniques and without excessive technical detail Supported by copious disciplinary examples, helping readers quickly adapt time series analysis to their area of study Covers both univariate and multivariate techniques in one volume Provides expert tips on, and helps mitigate common pitfalls of, powerful statistical software including EVIEWS and R Written in jargon-free and clear English from a master educator with 30 years+ experience explaining time series to novices Accompanied by a microsite with disciplinary data sets and files explaining how to build the calculations used in examples

Casanova's Lottery

Stephen M. Stigler
Casanova s Lottery Book PDF

Author : Stephen M. Stigler
Publisher : University of Chicago Press
Page : 252 pages
File Size : 53,9 Mb
Release : 2022-10-20
Category : History
ISBN : 9780226820781

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Casanova's Lottery by Stephen M. Stigler Pdf

The fascinating story of an important lottery that flourished in France from 1757 to 1836 and its role in transforming our understanding of the nature of risk. In the 1750s, at the urging of famed adventurer Giacomo Casanova, the French state began to embrace risk in adopting a new Loterie. The prize amounts paid varied, depending on the number of tickets bought and the amount of the bet, as determined by each individual bettor. The state could lose money on any individual Loterie drawing while being statistically guaranteed to come out on top in the long run. In adopting this framework, the French state took on risk in a way no other has, before or after. At each drawing the state was at risk of losing a large amount; what is more, that risk was precisely calculable, generally well understood, and yet taken on by the state with little more than a mathematical theory to protect it. Stephen M. Stigler follows the Loterie from its curious inception through its hiatus during the French Revolution, its renewal and expansion in 1797, and finally to its suppression in 1836, examining throughout the wider question of how members of the public came to trust in new financial technologies and believe in their value. Drawing from an extensive collection of rare ephemera, Stigler pieces together the Loterie’s remarkable inner workings, as well as its implications for the nature of risk and the role of lotteries in social life over the period 1700–1950. Both a fun read and fodder for many fields, Casanova's Lottery shines new light on the conscious introduction of risk into the management of a nation-state and the rationality of playing unfair games.

Statistics of Random Processes II

Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev
Statistics of Random Processes II Book PDF

Author : Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 47,5 Mb
Release : 2001
Category : Mathematics
ISBN : 3540639284

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Statistics of Random Processes II by Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev Pdf

"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW

Game-Theoretic Foundations for Probability and Finance

Glenn Shafer,Vladimir Vovk
Game Theoretic Foundations for Probability and Finance Book PDF

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 42,9 Mb
Release : 2019-03-21
Category : Business & Economics
ISBN : 9781118547939

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Game-Theoretic Foundations for Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

Trends in the Historiography of Science

K. Gavroglu,Y. Christianidis,Efthymios Nicolaides
Trends in the Historiography of Science Book PDF

Author : K. Gavroglu,Y. Christianidis,Efthymios Nicolaides
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 46,8 Mb
Release : 2013-04-18
Category : Science
ISBN : 9789401735964

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Trends in the Historiography of Science by K. Gavroglu,Y. Christianidis,Efthymios Nicolaides Pdf

The articles in this volume have been first presented during an international Conference organised by the Greek Society for the History of Science and Technology in June 1990 at Corfu. The Society was founded in 1989 and planned to hold a series of meetings to impress upon an audience comprised mainly by Greek students and scholars, the point that history of science is an autonomous discipline with its own plurality of approaches developed over the years as a result of long discussions and disputes within the community of historians of science. The Conference took place at a time when more and more people came to realise that the future of the Greek Universities and Research Centres depends not only on the progress of the institutional reforms, but also very crucially on the establishment of new and modern subject areas. Though there have been significant steps towards such a direction in the physical sciences, mathematics and engineering, the situation in the so-called humanities has been, at best, confusing. Political expediencies of the post war years and ideological commitments to a glorious, yet very distant past, paralysed the development of the humanities and constrained them within a framework which could not allow much more than a philological approach.

An Introduction to Survival Analysis Using Stata, Second Edition

Mario Cleves
An Introduction to Survival Analysis Using Stata Second Edition Book PDF

Author : Mario Cleves
Publisher : Stata Press
Page : 398 pages
File Size : 47,6 Mb
Release : 2008-05-15
Category : Computers
ISBN : 9781597180412

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An Introduction to Survival Analysis Using Stata, Second Edition by Mario Cleves Pdf

"[This book] provides new researchers with the foundation for understanding the various approaches for analyzing time-to-event data. This book serves not only as a tutorial for those wishing to learn survival analysis but as a ... reference for experienced researchers ..."--Book jacket.

Probability with Martingales

David Williams
Probability with Martingales Book PDF

Author : David Williams
Publisher : Cambridge University Press
Page : 274 pages
File Size : 53,5 Mb
Release : 1991-02-14
Category : Mathematics
ISBN : 0521406056

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Probability with Martingales by David Williams Pdf

This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory.

The Art of Causal Conjecture

Glenn Shafer
The Art of Causal Conjecture Book PDF

Author : Glenn Shafer
Publisher : MIT Press
Page : 554 pages
File Size : 41,9 Mb
Release : 1996
Category : Computers
ISBN : 026219368X

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The Art of Causal Conjecture by Glenn Shafer Pdf

In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy. The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes and high levels of precision in the measurement of their effects. The practical sciences -- medicine, business, engineering, and artificial intelligence -- must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both of these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making in the practical sciences. Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government, and science. The Art of Causal Conjecture shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated, and confronted by statistical evidence.

Probability and Finance

Glenn Shafer,Vladimir Vovk
Probability and Finance Book PDF

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 438 pages
File Size : 46,6 Mb
Release : 2005-02-25
Category : Business & Economics
ISBN : 9780471461715

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Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.

Central Banks as Economic Institutions

Jean-Philippe Touffut
Central Banks as Economic Institutions Book PDF

Author : Jean-Philippe Touffut
Publisher : Edward Elgar Publishing
Page : 233 pages
File Size : 48,6 Mb
Release : 2008-01-01
Category : Business & Economics
ISBN : 9781848445185

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Central Banks as Economic Institutions by Jean-Philippe Touffut Pdf

Theories and practices in central banking and monetary policy have changed radically over recent decades with independence and inflation targeting as the new keywords. This book offers interesting perspectives on the drivers of this development and its implication. It addresses contemporary questions on accountability, transparency and objectives for monetary policy as well as current policy problems related to globalization and financial imbalances. The book is topical, insightful and well written a must for everybody with an interest in central banking and monetary policy. Torben M. Andersen, University of Aarhus, Denmark The number of central banks in the world is approaching 180, a tenfold increase since the beginning of the twentieth century. What lies behind the spread of this economic institution? What underlying process has brought central banks to hold such a key role in economic life today? This book examines from a transatlantic perspective how the central bank has become the bank of banks. Thirteen distinguished economists and central bankers have been brought together to evaluate how central banks work, arrive at their policies, choose their instruments and gauge their success in managing economies, both in times of crisis and periods of growth. Central banks have gained greater independence from government control over the last 20 years. This widespread trend throws up new questions regarding the foundations, prerogatives and future of this economic institution. This book provides a better understanding of the current financial crisis through the in-depth study of the central bank. Researchers in the fields of monetary theory, monetary policy and central banking will find this volume of great interest. It will also appeal to students of economics, political economy, banking and finance, as well as economists, academics, and public policy advisers and analysts.

Handbook of Survival Analysis

John P. Klein,Hans C. van Houwelingen,Joseph G. Ibrahim,Thomas H. Scheike
Handbook of Survival Analysis Book PDF

Author : John P. Klein,Hans C. van Houwelingen,Joseph G. Ibrahim,Thomas H. Scheike
Publisher : CRC Press
Page : 635 pages
File Size : 47,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466555679

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Handbook of Survival Analysis by John P. Klein,Hans C. van Houwelingen,Joseph G. Ibrahim,Thomas H. Scheike Pdf

Handbook of Survival Analysis presents modern techniques and research problems in lifetime data analysis. This area of statistics deals with time-to-event data that is complicated by censoring and the dynamic nature of events occurring in time. With chapters written by leading researchers in the field, the handbook focuses on advances in survival analysis techniques, covering classical and Bayesian approaches. It gives a complete overview of the current status of survival analysis and should inspire further research in the field. Accessible to a wide range of readers, the book provides: An introduction to various areas in survival analysis for graduate students and novices A reference to modern investigations into survival analysis for more established researchers A text or supplement for a second or advanced course in survival analysis A useful guide to statistical methods for analyzing survival data experiments for practicing statisticians

Historiography of Mathematics in the 19th and 20th Centuries

Volker R. Remmert,Martina R. Schneider,Henrik Kragh Sørensen
Historiography of Mathematics in the 19th and 20th Centuries Book PDF

Author : Volker R. Remmert,Martina R. Schneider,Henrik Kragh Sørensen
Publisher : Birkhäuser
Page : 276 pages
File Size : 43,7 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9783319396491

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Historiography of Mathematics in the 19th and 20th Centuries by Volker R. Remmert,Martina R. Schneider,Henrik Kragh Sørensen Pdf

This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written. In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception. During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular. Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both a new professional identity and changes in its primary audience, various shifts of perspective in the way the history of mathematics was and is written can still be observed to this day. Initially concentrating on major internal, universal developments in certain sub-disciplines of mathematics, the field gradually gravitated towards a focus on contexts of knowledge production involving individuals, local practices, problems, communities, and networks. The goal of this book is to link these disciplinary and methodological changes in the history of mathematics to the broader cultural contexts of its practitioners, namely the historians of mathematics during the period in question.

A Mathematical Theory of Evidence

Glenn Shafer
A Mathematical Theory of Evidence Book PDF

Author : Glenn Shafer
Publisher : Princeton University Press
Page : 128 pages
File Size : 53,5 Mb
Release : 2020-06-30
Category : Mathematics
ISBN : 9780691214696

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A Mathematical Theory of Evidence by Glenn Shafer Pdf

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.