Overview
- Introduces readers to the theory of continuous-time stochastic processes using real-life examples in medicine, finance, and biology
- Includes updated exercises, examples, and material based on advances in recent literature
- Illustrates the ways that similar stochastic methods can be applied broadly across different fields
Part of the book series: Modeling and Simulation in Science, Engineering and Technology (MSSET)
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Table of contents (7 chapters)
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Front Matter
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Theory of Stochastic Processes
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Front Matter
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Applications of Stochastic Processes
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Front Matter
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Back Matter
Keywords
About this book
Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations.
An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. 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. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.
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Authors and Affiliations
About the authors
David Bakstein has been working in the financial industry for close to 25 years, many of those dedicated to applied mathematical models. He originally studied and taught at both the LSE and University of Oxford (OCIAM & Lady Margaret Hall).
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
DOI: https://doi.org/10.1007/978-3-030-69653-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-69652-8Published: 19 June 2021
Softcover ISBN: 978-3-030-69655-9Published: 20 June 2022
eBook ISBN: 978-3-030-69653-5Published: 18 June 2021
Series ISSN: 2164-3679
Series E-ISSN: 2164-3725
Edition Number: 4
Number of Pages: XXI, 560
Number of Illustrations: 14 b/w illustrations, 1 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Mathematical Modeling and Industrial Mathematics, Applications of Mathematics, Mathematical and Computational Biology