Stochastic Integration Theory
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Stochastic Integration Theory
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Author : Peter Medvegyev
language : en
Publisher: OUP Oxford
Release Date : 2007-07-26
Stochastic Integration Theory written by Peter Medvegyev and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-26 with Mathematics categories.
This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownian motion, Poisson process).
Stochastic Integration Theory
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Author : Péter Medvegyev
language : en
Publisher:
Release Date : 2023
Stochastic Integration Theory written by Péter Medvegyev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Stochastic integrals categories.
This graduate level text covers the theory of stochastic integration, an important area of Mathematics with a wide range of applications, including financial mathematics and signal processing.
Introduction To Stochastic Integration
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Author : K.L. Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Introduction To Stochastic Integration written by K.L. Chung 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 2013-11-09 with Mathematics categories.
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
Stochastic Integration In Banach Spaces
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Author : Vidyadhar Mandrekar
language : en
Publisher: Springer
Release Date : 2014-12-03
Stochastic Integration In Banach Spaces written by Vidyadhar Mandrekar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-03 with Mathematics categories.
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.
Introduction To Stochastic Integration
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Author : Hui-Hsiung Kuo
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-04
Introduction To Stochastic Integration written by Hui-Hsiung Kuo 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 2006-02-04 with Mathematics categories.
Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY
Stochastic Integration With Jumps
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Author : Klaus Bichteler
language : en
Publisher: Cambridge University Press
Release Date : 2002-05-13
Stochastic Integration With Jumps written by Klaus Bichteler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-13 with Mathematics categories.
The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
Vector Integration And Stochastic Integration In Banach Spaces
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Author : Nicolae Dinculeanu
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-28
Vector Integration And Stochastic Integration In Banach Spaces written by Nicolae Dinculeanu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.
A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.
Stochastic Integration And Differential Equations
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Author : Philip Protter
language : en
Publisher: Springer
Release Date : 2013-12-21
Stochastic Integration And Differential Equations written by Philip Protter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
Regularity And Integration Theory For A Class Of Stochastic Processes
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Author : Stefan Sperlich
language : en
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2012
Regularity And Integration Theory For A Class Of Stochastic Processes written by Stefan Sperlich and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
This book aims to develop a general integration theory for stochastic processes with stationary increments and spectral density. This class of motions particularly allows the simultaneous study of long-range dependence and intermittency effects and includes the most relevant random processes used in modern stochastic analysis. So for instance the Wiener process, the fractional Brownian motion, the fractional Riesz-Bessel motion but also Poisson and Levy processes. The so obtained knowledge on generalised stochastic integration will be used to achieve regularity results and is applied to parabolic Volterra problems with random noise as well as to the problem of anomalous diffusion with stochastic disturbance along the boundary.
Set Valued Stochastic Integrals And Applications
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Author : Michał Kisielewicz
language : en
Publisher: Springer Nature
Release Date : 2020-06-26
Set Valued Stochastic Integrals And Applications written by Michał Kisielewicz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-26 with Mathematics categories.
This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued Itô , set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings. The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.