Albert N 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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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

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ISBN 10

0387722068

ISBN 13

9780387722061

Optimal Stopping Rules

By: Albert N. Shiryaev

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Optimal Stopping Rules

By: Albert N. Shiryaev

Although three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.

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228

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Springer Science & Business Media

Published Date

ISBN 10

3540740112

ISBN 13

9783540740117

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

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ISBN 10

9810236050

ISBN 13

9789810236052

Problems in Probability

By: Albert N. Shiryaev

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Problems in Probability

By: Albert N. Shiryaev

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432

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ISBN 10

1461436885

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9781461436881

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

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ISBN 10

3540639292

ISBN 13

9783540639299

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

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

Statistics of Random Processes

I. General Theory

By: Robert S. Liptser,Albert N. Shiryaev

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Statistics of Random Processes

I. General Theory

By: Robert S. Liptser,Albert N. Shiryaev

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434

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Springer Science & Business Media

Published Date

ISBN 10

3662130432

ISBN 13

9783662130438

Probability-2

By: Albert N. Shiryaev

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Probability-2

By: Albert N. Shiryaev

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356

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ISBN 10

0387722084

ISBN 13

9780387722085

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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412

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Springer

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ISBN 10

3030015262

ISBN 13

9783030015268

Probability-1

By: Albert N. Shiryaev

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Probability-1

By: Albert N. Shiryaev

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501

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0387722068

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9780387722061

Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert N. Shiryaev

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Limit Theorems for Stochastic Processes

By: Jean Jacod,Albert N. Shiryaev

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

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620

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Springer Science & Business Media

Published Date

ISBN 10

3662025140

ISBN 13

9783662025147

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

Stochastic Disorder Problems

By: Albert N. Shiryaev

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Stochastic Disorder Problems

By: Albert N. Shiryaev

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412

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3030015262

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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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301

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9814494151

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9789814494151

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

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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

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450

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Springer Science & Business Media

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ISBN 10

3540639292

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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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852

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World Scientific

Published Date

ISBN 10

9810236050

ISBN 13

9789810236052

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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9814678600

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9789814678605

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 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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364

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ISBN 10

1441939326

ISBN 13

9781441939326

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