An Introduction to Continuous-Time Stochastic Processes
Theory, Models, and Applications to Finance, Biology, and Medicine
Authors: Capasso, Vincenzo, Bakstein, David
Free Preview- Provides a good balance between a rigorous mathematical approach and easy access to methods in applied research
- Revised and expanded edition includes new exercises, updated methodologies, and a new chapter on ergodic theory
- Minimal background knowledge of stochastic processes required
- Includes models of real world problems
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- About this Textbook
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This textbook, now in its third edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models New to the Third Edition: Infinitely divisible distributions Random measures Levy processes Fractional Brownian motion Ergodic theory Karhunen-Loeve expansion Additional applications Additional exercises Smoluchowski approximation of Langevin systems An Introduction to Continuous-Time Stochastic Processes, Third Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study 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. From reviews of previous editions: "The book 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
- About the authors
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Vincenzo Capasso is a Professor of Probability and Mathematical Statistics at the University of Milan. His research interests include spatially structured stochastic processes, stochastic geometry, reaction-diffusion systems, and statistics of structured stochastic processes. David Bakstein is a professor at the University of Milan, in ADAMSS (Interdisciplinary Center for Advanced Applied Mathematical and Statistical Sciences).
- Reviews
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“This is indeed a very well written book on stochastic processes and their numerous applications. … The reader will definitely benefit from the exercises given at the end of each of the chapters. … The book is strongly recommended to students following any graduate program in mathematics and mathematical modeling. University teachers can easily use this book as a possible reference book for special intermediate and advanced courses in stochastics and its applications.” (Jordan M. Stoyanov, zbMATH 1333.60002, 2016)
- Table of contents (7 chapters)
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Fundamentals of Probability
Pages 3-76
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Stochastic Processes
Pages 77-186
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The Itô Integral
Pages 187-229
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Stochastic Differential Equations
Pages 231-279
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Stability, Stationarity, Ergodicity
Pages 281-309
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- An Introduction to Continuous-Time 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
- 2015
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4939-2757-9
- DOI
- 10.1007/978-1-4939-2757-9
- Hardcover ISBN
- 978-1-4939-2756-2
- Softcover ISBN
- 978-1-4939-3836-0
- Series ISSN
- 2164-3679
- Edition Number
- 3
- Number of Pages
- XVI, 482
- Number of Illustrations
- 14 b/w illustrations
- Topics
