Albert Shiryaev's Books

Problems in Probability

By: Albert N. Shiryaev

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For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students. Many of the exercises included in the book contain helpful hints and other relevant information. Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book. This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.

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Page Count

432

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Springer Science & Business Media

Published Date

ISBN 10

1461436885

ISBN 13

9781461436881

Probability-1

By: Albert N. Shiryaev

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Probability-1

By: Albert N. Shiryaev

Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks and the Kalman-Bucy filter. Examples are discussed in detail, and there are a large number of exercises. This third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.

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501

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Springer

Published Date

ISBN 10

0387722068

ISBN 13

9780387722061

Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert Shiryaev

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Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert Shiryaev

This volume by two international leaders in the field proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. It emphasizes results that are useful for mathematical theory and mathematical statistics. Coverage develops in detail useful parts of the general theory of stochastic processes, such as martingale problems and absolute continuity or contiguity results.

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682

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Springer Science & Business Media

Published Date

ISBN 10

3662052652

ISBN 13

9783662052655

Statistical Experiments And Decision, Asymptotic Theory

By: Albert N Shiryaev,V G Spokoiny

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Statistical Experiments And Decision, Asymptotic Theory

By: Albert N Shiryaev,V G Spokoiny

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”.

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301

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World Scientific

Published Date

ISBN 10

9814494151

ISBN 13

9789814494151

Change Of Time And Change Of Measure (Second Edition)

By: Ole E Barndorff-nielsen,Albert N Shiryaev

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Change Of Time And Change Of Measure (Second Edition)

By: Ole E Barndorff-nielsen,Albert N Shiryaev

Change of Time and Change of Measure provides a comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law.Random change of time is key to understanding the nature of various stochastic processes, and gives rise to interesting mathematical results and insights of importance for the modeling and interpretation of empirically observed dynamic processes. Change of probability law is a technique for solving central questions in mathematical finance, and also has a considerable role in insurance mathematics, large deviation theory, and other fields.The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results relative to the existing literature, particularly with regard to mathematical finance.In this Second Edition a Chapter 13 entitled 'A Wider View' has been added. This outlines some of the developments that have taken place in the area of Change of Time and Change of Measure since the publication of the First Edition. Most of these developments have their root in the study of the Statistical Theory of Turbulence rather than in Financial Mathematics and Econometrics, and they form part of the new research area termed 'Ambit Stochastics'.

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345

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World Scientific Publishing Company

Published Date

ISBN 10

9814678600

ISBN 13

9789814678605

Statistics of Random Processes II

Applications

By: Robert S. Liptser,Albert N. Shiryaev

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Statistics of Random Processes II

Applications

By: Robert S. Liptser,Albert N. Shiryaev

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

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409

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Springer Science & Business Media

Published Date

ISBN 10

3662100282

ISBN 13

9783662100288

Essentials of Stochastic Finance

Facts, Models, Theory

By: Albert N. Shiryaev

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Essentials of Stochastic Finance

Facts, Models, Theory

By: Albert N. Shiryaev

Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.

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852

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World Scientific

Published Date

ISBN 10

9810236050

ISBN 13

9789810236052

Adaptive Algorithms and Stochastic Approximations

By: Albert Benveniste,Michel Metivier,Pierre Priouret

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Adaptive Algorithms and Stochastic Approximations

By: Albert Benveniste,Michel Metivier,Pierre Priouret

Adaptive systems are widely encountered in many applications ranging through adaptive filtering and more generally adaptive signal processing, systems identification and adaptive control, to pattern recognition and machine intelligence: adaptation is now recognised as keystone of "intelligence" within computerised systems. These diverse areas echo the classes of models which conveniently describe each corresponding system. Thus although there can hardly be a "general theory of adaptive systems" encompassing both the modelling task and the design of the adaptation procedure, nevertheless, these diverse issues have a major common component: namely the use of adaptive algorithms, also known as stochastic approximations in the mathematical statistics literature, that is to say the adaptation procedure (once all modelling problems have been resolved). The juxtaposition of these two expressions in the title reflects the ambition of the authors to produce a reference work, both for engineers who use these adaptive algorithms and for probabilists or statisticians who would like to study stochastic approximations in terms of problems arising from real applications. Hence the book is organised in two parts, the first one user-oriented, and the second providing the mathematical foundations to support the practice described in the first part. The book covers the topcis of convergence, convergence rate, permanent adaptation and tracking, change detection, and is illustrated by various realistic applications originating from these areas of applications.

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373

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Springer Science & Business Media

Published Date

ISBN 10

3642758940

ISBN 13

9783642758942

Statistical Testing Strategies in the Health Sciences

By: Albert Vexler,Alan D. Hutson,Xiwei Chen

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Statistical Testing Strategies in the Health Sciences

By: Albert Vexler,Alan D. Hutson,Xiwei Chen

Statistical Testing Strategies in the Health Sciences provides a compendium of statistical approaches for decision making, ranging from graphical methods and classical procedures through computationally intensive bootstrap strategies to advanced empirical likelihood techniques. It bridges the gap between theoretical statistical methods and practical procedures applied to the planning and analysis of health-related experiments. The book is organized primarily based on the type of questions to be answered by inference procedures or according to the general type of mathematical derivation. It establishes the theoretical framework for each method, with a substantial amount of chapter notes included for additional reference. It then focuses on the practical application for each concept, providing real-world examples that can be easily implemented using corresponding statistical software code in R and SAS. The book also explains the basic elements and methods for constructing correct and powerful statistical decision-making processes to be adapted for complex statistical applications. With techniques spanning robust statistical methods to more computationally intensive approaches, this book shows how to apply correct and efficient testing mechanisms to various problems encountered in medical and epidemiological studies, including clinical trials. Theoretical statisticians, medical researchers, and other practitioners in epidemiology and clinical research will appreciate the book’s novel theoretical and applied results. The book is also suitable for graduate students in biostatistics, epidemiology, health-related sciences, and areas pertaining to formal decision-making mechanisms.

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Page Count

622

Publisher

CRC Press

Published Date

ISBN 10

1315353016

ISBN 13

9781315353012

Quadratic and Hermitian Forms over Rings

By: Max-Albert Knus

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Quadratic and Hermitian Forms over Rings

By: Max-Albert Knus

From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.

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536

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Springer Science & Business Media

Published Date

ISBN 10

3642754015

ISBN 13

9783642754012

Optimal Stopping and Free-Boundary Problems

By: Goran Peskir,Albert Shiryaev

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Optimal Stopping and Free-Boundary Problems

By: Goran Peskir,Albert Shiryaev

This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

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515

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Springer Science & Business Media

Published Date

ISBN 10

3764373903

ISBN 13

9783764373900

Probability

By: Albert Shiryaev

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Probability

By: Albert Shiryaev

In the Preface to the first edition, originally published in 1980, we mentioned that this book was based on the author's lectures in the Department of Mechanics and Mathematics of the Lomonosov University in Moscow, which were issued, in part, in mimeographed form under the title "Probabil ity, Statistics, and Stochastic Processors, I, II" and published by that Univer sity. Our original intention in writing the first edition of this book was to divide the contents into three parts: probability, mathematical statistics, and theory of stochastic processes, which corresponds to an outline of a three semester course of lectures for university students of mathematics. However, in the course of preparing the book, it turned out to be impossible to realize this intention completely, since a full exposition would have required too much space. In this connection, we stated in the Preface to the first edition that only probability theory and the theory of random processes with discrete time were really adequately presented. Essentially all of the first edition is reproduced in this second edition. Changes and corrections are, as a rule, editorial, taking into account com ments made by both Russian and foreign readers of the Russian original and ofthe English and Germantranslations [Sll]. The author is grateful to all of these readers for their attention, advice, and helpful criticisms. In this second English edition, new material also has been added, as follows: in Chapter 111, §5, §§7-12; in Chapter IV, §5; in Chapter VII, §§8-10.

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636

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Springer Science & Business Media

Published Date

ISBN 10

1475725396

ISBN 13

9781475725391

Stochastic Disorder Problems

By: Albert N. Shiryaev

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Stochastic Disorder Problems

By: Albert N. Shiryaev

This monograph focuses on those stochastic quickest detection tasks in disorder problems that arise in the dynamical analysis of statistical data. These include quickest detection of randomly appearing targets, of spontaneously arising effects, and of arbitrage (in financial mathematics). There is also currently great interest in quickest detection methods for randomly occurring intrusions in information systems and in the design of defense methods against cyber-attacks. The author shows that the majority of quickest detection problems can be reformulated as optimal stopping problems where the stopping time is the moment the occurrence of disorder is signaled. Thus, considerable attention is devoted to the general theory of optimal stopping rules, and to its concrete problem-solving methods. The exposition covers both the discrete time case, which is in principle relatively simple and allows step-by-step considerations, and the continuous-time case, which often requires more technical machinery such as martingales, supermartingales, and stochastic integrals. There is a focus on the well-developed apparatus of Brownian motion, which enables the exact solution of many problems. The last chapter presents applications to financial markets. Researchers and graduate students interested in probability, decision theory and statistical sequential analysis will find this book useful.

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Page Count

412

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Springer

Published Date

ISBN 10

3030015262

ISBN 13

9783030015268

Statistical Experiments And Decision, Asymptotic Theory

By: Albert N Shiryaev,V G Spokoiny

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Statistical Experiments And Decision, Asymptotic Theory

By: Albert N Shiryaev,V G Spokoiny

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Page Count

301

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World Scientific

Published Date

ISBN 10

9814494151

ISBN 13

9789814494151

Change Of Time And Change Of Measure (Second Edition)

By: Ole E Barndorff-nielsen,Albert N Shiryaev

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Change Of Time And Change Of Measure (Second Edition)

By: Ole E Barndorff-nielsen,Albert N Shiryaev

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345

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World Scientific Publishing Company

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ISBN 10

9814678600

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9789814678605

Probability Theory III

Stochastic Calculus

By: Alʹbert Nikolaevich Shiri︠a︡ev

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Probability Theory III

Stochastic Calculus

By: Alʹbert Nikolaevich Shiri︠a︡ev

This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.

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272

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Springer Science & Business Media

Published Date

ISBN 10

3540546871

ISBN 13

9783540546870

Statistics of Random Processes

I. General Theory

By: Robert Liptser,Alʹbert Nikolaevich Shiri︠a︡ev,Albert N. Shiryaev

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Statistics of Random Processes

I. General Theory

By: Robert Liptser,Alʹbert Nikolaevich Shiri︠a︡ev,Albert N. Shiryaev

These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.

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450

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Springer Science & Business Media

Published Date

ISBN 10

3540639292

ISBN 13

9783540639299

Essentials of Stochastic Finance

Facts, Models, Theory

By: Albert N. Shiryaev

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Essentials of Stochastic Finance

Facts, Models, Theory

By: Albert N. Shiryaev

Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.

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Page Count

852

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World Scientific

Published Date

ISBN 10

9810236050

ISBN 13

9789810236052

Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert Shiryaev

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Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert Shiryaev

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682

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Springer Science & Business Media

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ISBN 10

3662052652

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9783662052655

Optimal Stopping and Free-Boundary Problems

By: Goran Peskir,Albert Shiryaev,Alʹbert Nikolaevich Shiri︠a︡ev

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Optimal Stopping and Free-Boundary Problems

By: Goran Peskir,Albert Shiryaev,Alʹbert Nikolaevich Shiri︠a︡ev

The book aims at disclosing a fascinating connection between optimal stopping problems in probability and free-boundary problems in analysis using minimal tools and focusing on key examples. The general theory of optimal stopping is exposed at the level of basic principles in both discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from classic ones (such as change of time, change of space, change of measure) to more recent ones (such as local time-space calculus and nonlinear integral equations). A detailed chapter on stochastic processes is included making the material more accessible to a wider cross-disciplinary audience. The book may be viewed as an ideal compendium for an interested reader who wishes to master stochastic calculus via fundamental examples. Areas of application where examples are worked out in full detail include financial mathematics, financial engineering, mathematical statistics, and stochastic analysis.

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Page Count

500

Publisher

Birkhäuser

Published Date

ISBN 10

3764324198

ISBN 13

9783764324193

Stochastic Finance

By: Albert N. Shiryaev,Maria do Rosário Grossinho,Paulo E. Oliveira,Manuel Leote Esquível

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Stochastic Finance

By: Albert N. Shiryaev,Maria do Rosário Grossinho,Paulo E. Oliveira,Manuel Leote Esquível

Since the pioneering work of Black, Scholes, and Merton in the field of financial mathematics, research has led to the rapid development of a substantial body of knowledge, with plenty of applications to the common functioning of the world’s financial institutions. Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the high-tech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques.

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Page Count

364

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Springer

Published Date

ISBN 10

1441939326

ISBN 13

9781441939326

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