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Author : M. M. Rao
Publisher : Courier Corporation
Page : 320 pages
File Size : 41,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9780486296531
This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods. No prior knowledge of probability is assumed. Numerous problems, most with hints. 1981 edition.
Author : Shigeo Kusuoka
Publisher : Springer Nature
Page : 218 pages
File Size : 55,9 Mb
Release : 2020-10-20
Category : Mathematics
ISBN : 9789811588648
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob–Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler–Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations.
Author : Alexander Melnikov
Publisher : Springer Nature
Page : 214 pages
File Size : 40,5 Mb
Release : 2023-04-02
Category : Mathematics
ISBN : 9783031253263
The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.
Author : Zdzislaw Brzezniak,Tomasz Zastawniak
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105336
Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.
Author : Weinan E,Tiejun Li,Eric Vanden-Eijnden
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 51,5 Mb
Release : 2019-05-28
Category : Stochastic analysis
ISBN : 9781470449339
This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.
Author : Vigirdas Mackevicius
Publisher : John Wiley & Sons
Page : 220 pages
File Size : 53,5 Mb
Release : 2013-02-07
Category : Mathematics
ISBN : 9781118603246
This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.
Author : Peter Watts Jones,Peter Smith
Publisher : CRC Press
Page : 255 pages
File Size : 45,8 Mb
Release : 2017-10-30
Category : Mathematics
ISBN : 9781498778121
Based on a well-established and popular course taught by the authors over many years, Stochastic Processes: An Introduction, Third Edition, discusses the modelling and analysis of random experiments, where processes evolve over time. The text begins with a review of relevant fundamental probability. It then covers gambling problems, random walks, and Markov chains. The authors go on to discuss random processes continuous in time, including Poisson, birth and death processes, and general population models, and present an extended discussion on the analysis of associated stationary processes in queues. The book also explores reliability and other random processes, such as branching, martingales, and simple epidemics. A new chapter describing Brownian motion, where the outcomes are continuously observed over continuous time, is included. Further applications, worked examples and problems, and biographical details have been added to this edition. Much of the text has been reworked. The appendix contains key results in probability for reference. This concise, updated book makes the material accessible, highlighting simple applications and examples. A solutions manual with fully worked answers of all end-of-chapter problems, and Mathematica® and R programs illustrating many processes discussed in the book, can be downloaded from crcpress.com.
Author : Michel Métivier
Publisher : Walter de Gruyter
Page : 305 pages
File Size : 49,5 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 9783110845563
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 52,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461203872
Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.
Author : Giuseppe Da Prato
Publisher : Springer
Page : 279 pages
File Size : 47,9 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9788876424991
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.
Author : Samuel Karlin,Howard E. Taylor
Publisher : Academic Press
Page : 557 pages
File Size : 53,5 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780080570419
The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other. The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.
Author : J. Michael Steele
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493054
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH
Author : X. Sheldon Lin,Society of Actuaries
Publisher : John Wiley & Sons
Page : 224 pages
File Size : 48,8 Mb
Release : 2006-04-21
Category : Mathematics
ISBN : 9780471793205
Incorporates the many tools needed for modeling and pricing infinance and insurance Introductory Stochastic Analysis for Finance and Insuranceintroduces readers to the topics needed to master and use basicstochastic analysis techniques for mathematical finance. The authorpresents the theories of stochastic processes and stochasticcalculus and provides the necessary tools for modeling and pricingin finance and insurance. Practical in focus, the book's emphasisis on application, intuition, and computation, rather thantheory. Consequently, the text is of interest to graduate students,researchers, and practitioners interested in these areas. While thetext is self-contained, an introductory course in probabilitytheory is beneficial to prospective readers. This book evolved from the author's experience as an instructor andhas been thoroughly classroom-tested. Following an introduction,the author sets forth the fundamental information and tools neededby researchers and practitioners working in the financial andinsurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics andApplications in Insurance, are devoted to more advanced topics.Readers learn the Feynman-Kac formula, the Girsanov's theorem, andcomplex barrier hitting times distributions. Finally, readersdiscover how stochastic analysis and principles are applied inpractice through two insurance examples: valuation of equity-linkedannuities under a stochastic interest rate environment andcalculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplifycomplex theory and pro-cesses. An extensive bibliography opens upadditional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, thistext is recommended for one-semester courses in stochastic financeand calculus. It is also recommended as a study guide forprofessionals taking Causality Actuarial Society (CAS) and Societyof Actuaries (SOA) actuarial examinations.
Author : A. Goswami,B.V. Rao
Publisher : Springer
Page : 226 pages
File Size : 52,8 Mb
Release : 2006-09-15
Category : Mathematics
ISBN : 9789386279316
Author : Gopinath Kallianpur,P Sundar
Publisher : OUP Oxford
Page : 368 pages
File Size : 50,9 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9780191004520
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.