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Modeling and Simulation in Science, Engineering and Technology

An Introduction to Continuous-Time Stochastic Processes

Theory, Models, and Applications to Finance, Biology, and Medicine

Authors: Capasso, Vincenzo, Bakstein, David

  • 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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Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4939-2757-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4939-2756-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4939-3836-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

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

“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)

  • Fundamentals of Probability

    Capasso, Vincenzo (et al.)

    Pages 3-76

  • Stochastic Processes

    Capasso, Vincenzo (et al.)

    Pages 77-186

  • The Itô Integral

    Capasso, Vincenzo (et al.)

    Pages 187-229

  • Stochastic Differential Equations

    Capasso, Vincenzo (et al.)

    Pages 231-279

  • Stability, Stationarity, Ergodicity

    Capasso, Vincenzo (et al.)

    Pages 281-309

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4939-2757-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-1-4939-2756-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-1-4939-3836-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
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 and Tables
14 b/w illustrations
Topics