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An Introduction to Continuous-Time Stochastic Processes

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

  • Textbook
  • © 2015

Overview

Authors:
  1. Vincenzo Capasso

    1. ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences), Università degli Studi di Milano, Milan, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. David Bakstein

    1. ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences), Università degli Studi di Milano, Milan, Italy

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Theory of Stochastic Processes

    1. Front Matter

      Pages 1-1
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    2. Fundamentals of Probability

      • Vincenzo Capasso, David Bakstein
      Pages 3-76

    3. Stochastic Processes

      • Vincenzo Capasso, David Bakstein
      Pages 77-186

    4. The Itô Integral

      • Vincenzo Capasso, David Bakstein
      Pages 187-229

    5. Stochastic Differential Equations

      • Vincenzo Capasso, David Bakstein
      Pages 231-279

    6. Stability, Stationarity, Ergodicity

      • Vincenzo Capasso, David Bakstein
      Pages 281-309

  3. Applications of Stochastic Processes

    1. Front Matter

      Pages 311-311
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    2. Applications to Finance and Insurance

      • Vincenzo Capasso, David Bakstein
      Pages 313-348

    3. Applications to Biology and Medicine

      • Vincenzo Capasso, David Bakstein
      Pages 349-400

  4. Back Matter

    Pages 401-482
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Keywords

About this book

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 ofinterest 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

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)

Authors and Affiliations

  • ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences), Università degli Studi di Milano, Milan, Italy

    Vincenzo Capasso, David Bakstein

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).

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