Introduction To Stochastic Calculus

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Introduction to Stochastic Calculus with Applications

Fima C. Klebaner
Introduction to Stochastic Calculus with Applications Book PDF

Author : Fima C. Klebaner
Publisher : Imperial College Press
Page : 431 pages
File Size : 55,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945557

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Introduction to Stochastic Calculus with Applications by Fima C. Klebaner Pdf

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

Rajeeva L. Karandikar,B. V. Rao
Introduction to Stochastic Calculus Book PDF

Author : Rajeeva L. Karandikar,B. V. Rao
Publisher : Springer
Page : 441 pages
File Size : 44,8 Mb
Release : 2018-06-01
Category : Mathematics
ISBN : 9789811083181

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Introduction to Stochastic Calculus by Rajeeva L. Karandikar,B. V. Rao Pdf

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

Dieter Sondermann
Introduction to Stochastic Calculus for Finance Book PDF

Author : Dieter Sondermann
Publisher : Springer Science & Business Media
Page : 144 pages
File Size : 54,5 Mb
Release : 2006-12-02
Category : Business & Economics
ISBN : 9783540348375

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Introduction to Stochastic Calculus for Finance by Dieter Sondermann Pdf

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

Paolo Baldi
Stochastic Calculus Book PDF

Author : Paolo Baldi
Publisher : Springer
Page : 627 pages
File Size : 44,8 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9783319622262

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Stochastic Calculus by Paolo Baldi Pdf

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.

An Introduction to Quantum Stochastic Calculus

K.R. Parthasarathy
An Introduction to Quantum Stochastic Calculus Book PDF

Author : K.R. Parthasarathy
Publisher : Birkhäuser
Page : 299 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886413

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An Introduction to Quantum Stochastic Calculus by K.R. Parthasarathy Pdf

"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 and Financial Applications

J. Michael Steele
Stochastic Calculus and Financial Applications Book PDF

Author : J. Michael Steele
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493054

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Stochastic Calculus and Financial Applications by J. Michael Steele Pdf

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 Integration

K.L. Chung,R.J. Williams
Introduction to Stochastic Integration Book PDF

Author : K.L. Chung,R.J. Williams
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 55,9 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781461495871

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Introduction to Stochastic Integration by K.L. Chung,R.J. Williams Pdf

A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected Brownian motion, and time change are discussed. New to the second edition are a discussion of the Cameron–Martin–Girsanov transformation and a final chapter which provides an introduction to stochastic differential equations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematicians, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also proves that stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has become one of the most powerful tools in modern probability theory. —Journal of the American Statistical Association An attractive text...written in [a] lean and precise style...eminently readable. Especially pleasant are the care and attention devoted to details... A very fine book. —Mathematical Reviews

Elementary Stochastic Calculus with Finance in View

Thomas Mikosch
Elementary Stochastic Calculus with Finance in View Book PDF

Author : Thomas Mikosch
Publisher : World Scientific
Page : 230 pages
File Size : 43,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9810235437

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Elementary Stochastic Calculus with Finance in View by Thomas Mikosch Pdf

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.

Brownian Motion, Martingales, and Stochastic Calculus

Jean-François Le Gall
Brownian Motion Martingales and Stochastic Calculus Book PDF

Author : Jean-François Le Gall
Publisher : Springer
Page : 273 pages
File Size : 42,6 Mb
Release : 2016-04-28
Category : Mathematics
ISBN : 9783319310893

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Brownian Motion, Martingales, and Stochastic Calculus by Jean-François Le Gall Pdf

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.

Brownian Motion

René L. Schilling,Lothar Partzsch
Brownian Motion Book PDF

Author : René L. Schilling,Lothar Partzsch
Publisher : Walter de Gruyter GmbH & Co KG
Page : 424 pages
File Size : 54,6 Mb
Release : 2014-06-18
Category : Mathematics
ISBN : 9783110307306

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Brownian Motion by René L. Schilling,Lothar Partzsch Pdf

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.

Stochastic Calculus

Richard Durrett
Stochastic Calculus Book PDF

Author : Richard Durrett
Publisher : CRC Press
Page : 353 pages
File Size : 49,8 Mb
Release : 2018-03-29
Category : Mathematics
ISBN : 9781351413756

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Stochastic Calculus by Richard Durrett Pdf

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.

Introduction to Stochastic Processes with R

Robert P. Dobrow
Introduction to Stochastic Processes with R Book PDF

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
Page : 503 pages
File Size : 54,5 Mb
Release : 2016-03-07
Category : Mathematics
ISBN : 9781118740651

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Introduction to Stochastic Processes with R by Robert P. Dobrow Pdf

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.

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

Ovidiu Calin
Informal Introduction To Stochastic Calculus With Applications An Second Edition Book PDF

Author : Ovidiu Calin
Publisher : World Scientific
Page : 510 pages
File Size : 55,5 Mb
Release : 2021-11-15
Category : Mathematics
ISBN : 9789811247118

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

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.

Introduction To Stochastic Calculus With Applications (3rd Edition)

Klebaner Fima C
Introduction To Stochastic Calculus With Applications 3rd Edition Book PDF

Author : Klebaner Fima C
Publisher : World Scientific Publishing Company
Page : 452 pages
File Size : 47,6 Mb
Release : 2012-03-21
Category : Mathematics
ISBN : 9781911298670

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Introduction To Stochastic Calculus With Applications (3rd Edition) by Klebaner Fima C Pdf

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises./a

Brownian Motion and Stochastic Calculus

Ioannis Karatzas,Steven Shreve
Brownian Motion and Stochastic Calculus Book PDF

Author : Ioannis Karatzas,Steven Shreve
Publisher : Springer
Page : 490 pages
File Size : 55,7 Mb
Release : 2014-03-27
Category : Mathematics
ISBN : 9781461209492

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Brownian Motion and Stochastic Calculus by Ioannis Karatzas,Steven Shreve Pdf

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.