An Introduction to ContinuousTime Stochastic Processes
Theory, Models, and Applications to Finance, Biology, and Medicine
Authors: Capasso, Vincenzo, Bakstein, David
Free Preview A rigorous and selfcontained introduction to the theory of continuoustime stochastic processes
 Concrete examples of modeling realworld problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods
 Exercises at the end of each chapter; no previous knowledge of stochastic processes is required
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 About this Textbook

This concisely written book is a rigorous and selfcontained introduction to the theory of continuoustime stochastic processes. A balance of theory and applications, the work features concrete examples of modeling realworld problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.
Key topics covered include:
* Interacting particles and agentbased models: from polymers to ants
* Population dynamics: from birth and death processes to epidemics
* Financial market models: the nonarbitrage principle
* Contingent claim valuation models: the riskneutral valuation theory
* Risk analysis in insurance
An Introduction to ContinuousTime Stochastic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for selfstudy or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided.
 Reviews

"This is an introductory text on continuous time stochastic processes and their applications to finance and biology. The first part of the book reviews basic probability and then covers the basic continuous time processes such as Brownian motion, point processes, etc.... The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications." —Mathematical Reviews
"The book is a systematic, rigorous, and selfcontained introduction to the theory of continuoustime stochastic processes. It is an account of fundamental concepts as they appear in relevant modern applications and literature.... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications." —Zentralblatt MATH
"This book provides a mathematical overview of the theory of continuoustime stochastic processes, with emphasis on stochastic differential equations (SDEs). Applications in finance and population modelling are also briefly reviewed.... The primary audience for this book will be mathematicians (both pure and applied) active in other areas who require an introduction to stochastic theory. Scientists already working in the applications of SDEs will also benefit from this mathematically rigorous reference text. The core of the text on Ito calculus...would be suitable supplementary reading for graduate or advanced undergraduate students of stochastic theory.... The style of the text...is concise and rigorous.... Each chapter concludes with a set of exercises inviting readers to prove supplementary results and review particular aspects of the theory.... In summary, I have found this to be a useful reference text, and would recommend it to those wishing to delve into the mathematical theory of stochastic processes." —UK Nonlinear News
"This book covers an extensive part of probability theory, the theory for timecontinuous stochastic processes, and also gives a lot of examples from finance, biology, and medicine.... Most of the contents of the book have been used as lecture material for several years, which is evident by the fact that there are very few misprints, and the text is wellstructured also having a good labelling system.... [T]he book is quite compact covering the fundamentals in probability theory and stochastic processes in 200 pages.... The chapter on applications towards finance covers many classical models such as arbitragefree markets, [the] Black–Scholes model, and models for interest and ruin probabilities. This chapter is probably the best in the book.... The chapter on applications towards biology and medicine…contains models for epidemics, individualbased models, and a model for neural activity.... After each chapter there are several exercises illustrating and extending the theory presented in the text. Many of these exercises are interesting and rewarding to solve." —Mathematical Biosciences
"The book is written in a systematic and selfcontained way where omitted details are compensated by references to a commonly accessible literature. The book is [geared] to students or professionals who want to get acquainted with the role of stochastic processes in modeling random phenomena in economics, biology, or medicine." —Applications of Mathematics
 Table of contents (6 chapters)


Fundamentals of Probability
Pages 350

Stochastic Processes
Pages 51126

The Itô Integral
Pages 127159

Stochastic Differential Equations
Pages 161208

Applications to Finance and Insurance
Pages 211238

Table of contents (6 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 An Introduction to ContinuousTime Stochastic Processes
 Book Subtitle
 Theory, Models, and Applications to Finance, Biology, and Medicine
 Authors

 Vincenzo Capasso
 David Bakstein
 Series Title
 Modeling and Simulation in Science, Engineering and Technology
 Copyright
 2005
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9780817644284
 DOI
 10.1007/b138900
 Series ISSN
 21643679
 Edition Number
 1
 Number of Pages
 XIV, 344
 Number of Illustrations
 13 b/w illustrations
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