Stochastic Processes And Calculus Explained

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Stochastic Processes And Calculus
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Author : Uwe Hassler
language : en
Publisher: Springer
Release Date : 2015-12-12
Stochastic Processes And Calculus written by Uwe Hassler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-12 with Business & Economics categories.
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 Calculus
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Author : Paolo Baldi
language : en
Publisher: Springer
Release Date : 2017-11-09
Stochastic Calculus written by Paolo Baldi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
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 With Applications
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Author : Fima C. Klebaner
language : en
Publisher: Imperial College Press
Release Date : 2005
Introduction To Stochastic Calculus With Applications written by Fima C. Klebaner and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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 Processes And Calculus Explained
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Author : Vikas Rathi
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Stochastic Processes And Calculus Explained written by Vikas Rathi and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Stochastic Processes and Calculus Explained" is an essential textbook designed to help readers understand and apply stochastic processes across various fields. Written in clear, accessible language, this book provides a solid foundation in probability theory and calculus while diving into stochastic processes, including random variables, probability distributions, Brownian motion, stochastic integration, and stochastic differential equations. We emphasize the practical relevance of these concepts in finance, physics, engineering, and biology. Our guide illustrates how stochastic processes model uncertainty and randomness, aiding in informed decision-making, outcome prediction, and complex system analysis. With real-world examples and exercises, we ensure readers can grasp and apply these concepts effectively. The book offers a strong mathematical foundation, covering key tools and techniques such as probability theory, calculus, and linear algebra, essential for understanding stochastic processes. Catering to readers of all backgrounds and expertise levels, "Stochastic Processes and Calculus Explained" is ideal for beginners and experienced practitioners alike. Its clear explanations, intuitive coverage, and comprehensive approach make it an invaluable resource for students, researchers, and professionals worldwide.
Introduction To Stochastic Analysis And Malliavin Calculus
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Author : Giuseppe Da Prato
language : en
Publisher: Springer
Release Date : 2008
Introduction To Stochastic Analysis And Malliavin Calculus written by Giuseppe Da Prato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material has grown from courses delivered at the Scuola Normale Superiore di Pisa and has been refined over several years of teaching experience.
Informal Introduction To Stochastic Calculus With Applications An Second Edition
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Author : Ovidiu Calin
language : en
Publisher: World Scientific
Release Date : 2021-11-15
Informal Introduction To Stochastic Calculus With Applications An Second Edition written by Ovidiu Calin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-15 with Mathematics categories.
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.
Brownian Motion And Stochastic Calculus
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Author : Ioannis Karatzas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Brownian Motion And Stochastic Calculus written by Ioannis Karatzas 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 2012-12-06 with Mathematics categories.
Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuous time context. It has been our goal to write a systematic and thorough exposi tion of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion.
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.
Stochastic Calculus For Finance I
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Author : Steven Shreve
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-21
Stochastic Calculus For Finance I written by Steven Shreve 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 2004-04-21 with Mathematics categories.
Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance
Stochastic Calculus Of Variations In Mathematical Finance
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Author : Paul Malliavin
language : en
Publisher: Springer
Release Date : 2010-11-30
Stochastic Calculus Of Variations In Mathematical Finance written by Paul Malliavin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-30 with Business & Economics categories.
Highly esteemed author Topics covered are relevant and timely