Robert Liptser's Books

Statistics of Random Processes II

II. Applications

By: Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev

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Statistics of Random Processes II

II. Applications

By: Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev

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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Page Count

428

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540639284

ISBN 13

9783540639282

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

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Page Count

409

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Springer Science & Business Media

Published Date

ISBN 10

3662100282

ISBN 13

9783662100288

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

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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Page Count

434

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662130432

ISBN 13

9783662130438

Schrödinger Diffusion Processes

By: Robert Aebi

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Schrödinger Diffusion Processes

By: Robert Aebi

In 1931 Erwin Schrödinger considered the following problem: A huge cloud of independent and identical particles with known dynamics is supposed to be observed at finite initial and final times. What is the "most probable" state of the cloud at intermediate times? The present book provides a general yet comprehensive discourse on Schrödinger's question. Key roles in this investigation are played by conditional diffusion processes, pairs of non-linear integral equations and interacting particles systems. The introductory first chapter gives some historical background, presents the main ideas in a rather simple discrete setting and reveals the meaning of intermediate prediction to quantum mechanics. In order to answer Schrödinger's question, the book takes three distinct approaches, dealt with in separate chapters: transformation by means of a multiplicative functional, projection by means of relative entropy, and variation of a functional associated to pairs of non-linear integral equations. The book presumes a graduate level of knowledge in mathematics or physics and represents a relevant and demanding application of today's advanced probability theory.

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Page Count

196

Publisher

Birkhäuser

Published Date

ISBN 10

3034890273

ISBN 13

9783034890274

Stochastic Networks and Queues

By: Philippe Robert

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Stochastic Networks and Queues

By: Philippe Robert

Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.

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406

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662130521

ISBN 13

9783662130520

Stochastic Portfolio Theory

By: E. Robert Fernholz

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Stochastic Portfolio Theory

By: E. Robert Fernholz

Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.

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Page Count

190

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475736991

ISBN 13

9781475736991

Financial Derivatives Pricing

Selected Works of Robert Jarrow

By: Robert A. Jarrow

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Financial Derivatives Pricing

Selected Works of Robert Jarrow

By: Robert A. Jarrow

This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous HeathOCoJarrowOCoMorton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.

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Page Count

609

Publisher

World Scientific

Published Date

ISBN 10

9812819223

ISBN 13

9789812819222

An Introduction to Statistical Signal Processing

By: Robert M. Gray,Lee D. Davisson

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An Introduction to Statistical Signal Processing

By: Robert M. Gray,Lee D. Davisson

This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

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Page Count

479

Publisher

Cambridge University Press

Published Date

ISBN 10

1139456288

ISBN 13

9781139456289

Stochastic Calculus and Applications

By: Samuel N. Cohen,Robert J. Elliott

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Stochastic Calculus and Applications

By: Samuel N. Cohen,Robert J. Elliott

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)

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Page Count

673

Publisher

Birkhäuser

Published Date

ISBN 10

1493928678

ISBN 13

9781493928675

Hidden Markov Models

Estimation and Control

By: Robert J. Elliott,Lakhdar Aggoun,John B. Moore

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Hidden Markov Models

Estimation and Control

By: Robert J. Elliott,Lakhdar Aggoun,John B. Moore

The authors begin with discrete time and discrete state spaces. From there, they proceed to cover continuous time, and progress from linear models to nonlinear models, and from completely known models to only partially known models.

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374

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387943641

ISBN 13

9780387943640

Theory of Martingales

By: Robert Liptser,A.N. Shiryayev

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Theory of Martingales

By: Robert Liptser,A.N. Shiryayev

One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

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Page Count

806

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Springer Science & Business Media

Published Date

ISBN 10

9400924380

ISBN 13

9789400924383

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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Page Count

450

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540639292

ISBN 13

9783540639299

Book's by Robert Liptser

Statistics of Random Processes II

Statistics of Random Processes II

Statistics of Random Processes II

Statistics of Random Processes II

Statistics of Random Processes

Statistics of Random Processes

Schrödinger Diffusion Processes

Schrödinger Diffusion Processes

Stochastic Networks and Queues

Stochastic Networks and Queues

Stochastic Portfolio Theory

Stochastic Portfolio Theory

Financial Derivatives Pricing

Financial Derivatives Pricing

An Introduction to Statistical Signal Processing

An Introduction to Statistical Signal Processing

Stochastic Calculus and Applications

Stochastic Calculus and Applications

Hidden Markov Models

Hidden Markov Models

Theory of Martingales

Theory of Martingales

Statistics of Random Processes

Statistics of Random Processes

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