Introduction To Stochastic Calculus

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Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Introduction To Stochastic Calculus With Applications (2nd Edition)

Author : Fima C Klebaner
Publisher : World Scientific Publishing Company
ISBN 13 : 1848168225
Total Pages : 432 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Introduction To Stochastic Calculus With Applications (2nd Edition) by : Fima C Klebaner

Download or read book Introduction To Stochastic Calculus With Applications (2nd Edition) written by Fima C Klebaner and published by World Scientific Publishing Company. This book was released on 2005-06-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author./a

随机分析及应用

Author : Fima C. Klebaner
Publisher :
ISBN 13 : 9787115183446
Total Pages : 416 pages
Book Rating : 4.1/5 (834 download)

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Book Synopsis 随机分析及应用 by : Fima C. Klebaner

Download or read book 随机分析及应用 written by Fima C. Klebaner and published by . This book was released on 2005 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 本书介绍了随机分析的理论和应用两方面的知识,内容涉及积分和概率论的基础知识、基本的随机过程、布朗运动和伊藤过程的积分、随机微分方程、半鞅积分、纯离散过程,以及随机分析在金融、生物、工程和物理等方面的应用。书中有大量的例题和习题集,并附有答案。

Stochastic Calculus

Author : Paolo Baldi
Publisher : Springer
ISBN 13 : 3319622269
Total Pages : 627 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Stochastic Calculus by : Paolo Baldi

Download or read book Stochastic Calculus written by Paolo Baldi and published by Springer. This book was released on 2017-11-09 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.

Introduction to Stochastic Calculus

Author : Rajeeva L. Karandikar
Publisher : Springer
ISBN 13 : 9811083185
Total Pages : 441 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Introduction to Stochastic Calculus by : Rajeeva L. Karandikar

Download or read book Introduction to Stochastic Calculus written by Rajeeva L. Karandikar and published by Springer. This book was released on 2018-06-01 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

Introduction to Stochastic Calculus for Finance

Author : Dieter Sondermann
Publisher : Springer Science & Business Media
ISBN 13 : 3540348379
Total Pages : 144 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Introduction to Stochastic Calculus for Finance by : Dieter Sondermann

Download or read book Introduction to Stochastic Calculus for Finance written by Dieter Sondermann and published by Springer Science & Business Media. This book was released on 2006-12-02 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there are many textbooks on stochastic calculus applied to finance, this volume earns its place with a pedagogical approach. The text presents a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader should be familiar with elementary real analysis and basic probability theory.

Stochastic Calculus and Financial Applications

Author : J. Michael Steele
Publisher : Springer Science & Business Media
ISBN 13 : 1468493051
Total Pages : 303 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Stochastic Calculus and Financial Applications by : J. Michael Steele

Download or read book Stochastic Calculus and Financial Applications written by J. Michael Steele and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Stochastic Processes

Author : Erhan Cinlar
Publisher : Courier Corporation
ISBN 13 : 0486276325
Total Pages : 418 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Introduction to Stochastic Processes by : Erhan Cinlar

Download or read book Introduction to Stochastic Processes written by Erhan Cinlar and published by Courier Corporation. This book was released on 2013-02-20 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear presentation employs methods that recognize computer-related aspects of theory. Topics include expectations and independence, Bernoulli processes and sums of independent random variables, Markov chains, renewal theory, more. 1975 edition.

An Introduction to Quantum Stochastic Calculus

Author : K.R. Parthasarathy
Publisher : Birkhäuser
ISBN 13 : 3034886411
Total Pages : 299 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis An Introduction to Quantum Stochastic Calculus by : K.R. Parthasarathy

Download or read book An Introduction to Quantum Stochastic Calculus written by K.R. Parthasarathy and published by Birkhäuser. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.

Stochastic Calculus

Author : Richard Durrett
Publisher : CRC Press
ISBN 13 : 9780849380716
Total Pages : 356 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Stochastic Calculus by : Richard Durrett

Download or read book Stochastic Calculus written by Richard Durrett and published by CRC Press. This book was released on 1996-06-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions. The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.

Stochastic Calculus

Author : Richard Durrett
Publisher : CRC Press
ISBN 13 : 1351413759
Total Pages : 353 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Stochastic Calculus by : Richard Durrett

Download or read book Stochastic Calculus written by Richard Durrett and published by CRC Press. This book was released on 2018-03-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions. The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.

Brownian Motion

Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110307308
Total Pages : 424 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Brownian Motion by : René L. Schilling

Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-06-18 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

Brownian Motion, Martingales, and Stochastic Calculus

Author : Jean-François Le Gall
Publisher : Springer
ISBN 13 : 3319310895
Total Pages : 273 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Brownian Motion, Martingales, and Stochastic Calculus by : Jean-François Le Gall

Download or read book Brownian Motion, Martingales, and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Informal Introduction To Stochastic Calculus With Applications, An (Second Edition)

Author : Ovidiu Calin
Publisher : World Scientific
ISBN 13 : 9811247110
Total Pages : 510 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Informal Introduction To Stochastic Calculus With Applications, An (Second Edition) by : Ovidiu Calin

Download or read book Informal Introduction To Stochastic Calculus With Applications, An (Second Edition) written by Ovidiu Calin and published by World Scientific. This book was released on 2021-11-15 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.This edition has also improved presentation from the first edition in several chapters, including new material.

Elementary Stochastic Calculus with Finance in View

Author : Thomas Mikosch
Publisher : World Scientific
ISBN 13 : 9789810235437
Total Pages : 230 pages
Book Rating : 4.2/5 (354 download)

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Book Synopsis Elementary Stochastic Calculus with Finance in View by : Thomas Mikosch

Download or read book Elementary Stochastic Calculus with Finance in View written by Thomas Mikosch and published by World Scientific. This book was released on 1998 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Introduction to Stochastic Processes with R

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
ISBN 13 : 1118740653
Total Pages : 503 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Introduction to Stochastic Processes with R by : Robert P. Dobrow

Download or read book Introduction to Stochastic Processes with R written by Robert P. Dobrow and published by John Wiley & Sons. This book was released on 2016-03-07 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.

Stochastic Processes and Calculus

Author : Uwe Hassler
Publisher : Springer
ISBN 13 : 3319234285
Total Pages : 391 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Stochastic Processes and Calculus by : Uwe Hassler

Download or read book Stochastic Processes and Calculus written by Uwe Hassler and published by Springer. This book was released on 2015-12-12 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes. This introduction is elementary and rigorous at the same time. On the one hand it gives a basic and illustrative presentation of the relevant topics without using many technical derivations. On the other hand many of the procedures are presented at a technically advanced level: for a thorough understanding, they are to be proven. In order to meet both requirements jointly, the present book is equipped with a lot of challenging problems at the end of each chapter as well as with the corresponding detailed solutions. Thus the virtual text - augmented with more than 60 basic examples and 40 illustrative figures - is rather easy to read while a part of the technical arguments is transferred to the exercise problems and their solutions.