Semimartingale Theory And Stochastic Calculus
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Semimartingale Theory And Stochastic Calculus
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Author : Sheng-wu He
language : en
Publisher: Taylor & Francis
Release Date : 1992
Semimartingale Theory And Stochastic Calculus written by Sheng-wu He and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Semimartingales categories.
Semimartingale Theory And Stochastic Calculus
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Author : Sheng-Wu He
language : en
Publisher: Routledge
Release Date : 2019-07-09
Semimartingale Theory And Stochastic Calculus written by Sheng-Wu He and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-09 with Mathematics categories.
Semimartingale Theory and Stochastic Calculus presents a systematic and detailed account of the general theory of stochastic processes, the semimartingale theory, and related stochastic calculus. The book emphasizes stochastic integration for semimartingales, characteristics of semimartingales, predictable representation properties and weak convergence of semimartingales. It also includes a concise treatment of absolute continuity and singularity, contiguity, and entire separation of measures by semimartingale approach. Two basic types of processes frequently encountered in applied probability and statistics are highlighted: processes with independent increments and marked point processes encountered frequently in applied probability and statistics. Semimartingale Theory and Stochastic Calculus is a self-contained and comprehensive book that will be valuable for research mathematicians, statisticians, engineers, and students.
Semimartingale Theory And Stochastic Calculus
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Author : Sheng-Wu He
language : en
Publisher:
Release Date : 1992
Semimartingale Theory And Stochastic Calculus written by Sheng-Wu He and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with MATHEMATICS categories.
Handbook Of Stochastic Analysis And Applications
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Author : D. Kannan
language : en
Publisher: CRC Press
Release Date : 2001-10-23
Handbook Of Stochastic Analysis And Applications written by D. Kannan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-23 with Mathematics categories.
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Limit Theorems For Stochastic Processes
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Limit Theorems For Stochastic Processes written by Jean Jacod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Brownian Motion Martingales And Stochastic Calculus
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Author : Jean-François Le Gall
language : en
Publisher: Springer
Release Date : 2016-04-28
Brownian Motion Martingales And Stochastic Calculus written by Jean-François Le Gall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Mathematics categories.
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 And Stochastic Calculus
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Author : Ioannis Karatzas
language : en
Publisher: Springer
Release Date : 2014-03-27
Brownian Motion And Stochastic Calculus written by Ioannis Karatzas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-27 with Mathematics categories.
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This 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 text is complemented by a large number of problems and exercises.
Introduction To Stochastic Calculus
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Author : Rajeeva L. Karandikar
language : en
Publisher: Springer
Release Date : 2018-06-01
Introduction To Stochastic Calculus written by Rajeeva L. Karandikar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Mathematics categories.
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.
Stochastic Calculus For Fractional Brownian Motion And Applications
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Author : Francesca Biagini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Stochastic Calculus For Fractional Brownian Motion And Applications written by Francesca Biagini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-17 with Mathematics categories.
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for fBm. 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.