An Introduction to Continuous-Time Stochastic Processes

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

  • Vincenzo Capasso
  • David Bakstein

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Theory of Stochastic Processes

    1. Front Matter
      Pages 1-1
    2. Vincenzo Capasso, David Bakstein
      Pages 3-76
    3. Vincenzo Capasso, David Bakstein
      Pages 77-171
    4. Vincenzo Capasso, David Bakstein
      Pages 173-212
    5. Vincenzo Capasso, David Bakstein
      Pages 213-273
  3. Applications of Stochastic Processes

    1. Front Matter
      Pages 275-275
    2. Vincenzo Capasso, David Bakstein
      Pages 277-310
    3. Vincenzo Capasso, David Bakstein
      Pages 311-358
  4. Back Matter
    Pages 359-434

About this book


From reviews of First Edition:

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

This is an introductory text on continuous time stochastic processes and their applications to finance and biology. ... 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

Revised and enhanced, this concisely written second edition of An Introduction to Continuous-Time Stochastic Processes is 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
* Agent-based models

New to the Second Edition:

* Improved presentation of original concepts
* Expanded background on probability theory
* Substantial material applicable to finance and biology, including stable laws, Lévy processes, and Itô-Lévy calculus
* Supplemental appendix to provide basic facts on semigroups of linear operators

An Introduction to Continuous-Time Stochastic Processes, Second 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.


Brownian motion Ito integral Levy process Markov process differential equations martingale point process population dynamics risk analysis stochastic processes

Authors and affiliations

  • Vincenzo Capasso
    • 1
  • David Bakstein
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)University of MilanMilanItaly

Bibliographic information

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