Stochastic Calculus And Applications

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Stochastic Calculus and Applications

Samuel N. Cohen,Robert J. Elliott
Stochastic Calculus and Applications Book PDF

Author : Samuel N. Cohen,Robert J. Elliott
Publisher : Birkhäuser
Page : 666 pages
File Size : 45,7 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9781493928675

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Stochastic Calculus and Applications by Samuel N. Cohen,Robert J. Elliott Pdf

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)

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 : 43,8 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.

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 : 42,5 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

Stochastic Calculus for Fractional Brownian Motion and Applications

Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
Stochastic Calculus for Fractional Brownian Motion and Applications Book PDF

Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 40,5 Mb
Release : 2008-02-17
Category : Mathematics
ISBN : 9781846287978

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Stochastic Calculus for Fractional Brownian Motion and Applications by Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang Pdf

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and 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 : 54,7 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.

Stochastic Calculus

Mircea Grigoriu
Stochastic Calculus Book PDF

Author : Mircea Grigoriu
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 43,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780817682286

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Stochastic Calculus by Mircea Grigoriu Pdf

Algebraic, differential, and integral equations are used in the applied sciences, en gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time. Generally, the coefficients of and/or the input to these equations are not precisely known be cause of insufficient information, limited understanding of some underlying phe nomena, and inherent randonmess. For example, the orientation of the atomic lattice in the grains of a polycrystal varies randomly from grain to grain, the spa tial distribution of a phase of a composite material is not known precisely for a particular specimen, bone properties needed to develop reliable artificial joints vary significantly with individual and age, forces acting on a plane from takeoff to landing depend in a complex manner on the environmental conditions and flight pattern, and stock prices and their evolution in time depend on a large number of factors that cannot be described by deterministic models. Problems that can be defined by algebraic, differential, and integral equations with random coefficients and/or input are referred to as stochastic problems. The main objective of this book is the solution of stochastic problems, that is, the determination of the probability law, moments, and/or other probabilistic properties of the state of a physical, economic, or social system. It is assumed that the operators and inputs defining a stochastic problem are specified.

Continuous Stochastic Calculus with Applications to Finance

Michael Meyer
Continuous Stochastic Calculus with Applications to Finance Book PDF

Author : Michael Meyer
Publisher : CRC Press
Page : 336 pages
File Size : 40,5 Mb
Release : 2000-10-25
Category : Mathematics
ISBN : 9781420035599

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Continuous Stochastic Calculus with Applications to Finance by Michael Meyer Pdf

The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale. The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives. Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.

Stochastic Differential Equations

Bernt Oksendal
Stochastic Differential Equations Book PDF

Author : Bernt Oksendal
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 42,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662130506

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Stochastic Differential Equations by Bernt Oksendal Pdf

These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Malliavin Calculus with Applications to Stochastic Partial Differential Equations

Marta Sanz-Sole
Malliavin Calculus with Applications to Stochastic Partial Differential Equations Book PDF

Author : Marta Sanz-Sole
Publisher : CRC Press
Page : 150 pages
File Size : 48,7 Mb
Release : 2005-08-17
Category : Mathematics
ISBN : 1439818940

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Malliavin Calculus with Applications to Stochastic Partial Differential Equations by Marta Sanz-Sole Pdf

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics. This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself based on a general Gaussian space, going from the simple, finite-dimensional setting to the infinite-dimensional one. The final three chapters discuss recent research on regularity of the solution of stochastic partial differential equations and the existence and smoothness of their probability laws. About the author: Marta Sanz-Solé is Professor at the Faculty of Mathematics, University of Barcelona. She is a leading member of the research group on stochastic analysis at Barcelona, and in 1998 she received the Narcis Monturiol Award of Scientific and Technological Excellence from the autonomous government of Catalonia.

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 : 51,6 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.

Stochastic Processes

Pierre Del Moral,Spiridon Penev
Stochastic Processes Book PDF

Author : Pierre Del Moral,Spiridon Penev
Publisher : CRC Press
Page : 866 pages
File Size : 50,5 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9781498701846

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Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Stochastic Processes and Calculus

Uwe Hassler
Stochastic Processes and Calculus Book PDF

Author : Uwe Hassler
Publisher : Springer
Page : 391 pages
File Size : 44,9 Mb
Release : 2015-12-12
Category : Business & Economics
ISBN : 9783319234281

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Stochastic Processes and Calculus by Uwe Hassler Pdf

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.

Stochastic Processes and Applications

Grigorios A. Pavliotis
Stochastic Processes and Applications Book PDF

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 339 pages
File Size : 52,5 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

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 : 54,9 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

Stochastic Processes with Applications to Finance

Masaaki Kijima
Stochastic Processes with Applications to Finance Book PDF

Author : Masaaki Kijima
Publisher : CRC Press
Page : 345 pages
File Size : 43,8 Mb
Release : 2016-04-19
Category : Business & Economics
ISBN : 9781439884843

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Stochastic Processes with Applications to Finance by Masaaki Kijima Pdf

Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools