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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-xvi
  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 77-186
    4. Vincenzo Capasso, David Bakstein
      Pages 187-229
    5. Vincenzo Capasso, David Bakstein
      Pages 231-279
    6. Vincenzo Capasso, David Bakstein
      Pages 281-309
  3. Applications of Stochastic Processes

    1. Front Matter
      Pages 311-311
    2. Vincenzo Capasso, David Bakstein
      Pages 313-348
    3. Vincenzo Capasso, David Bakstein
      Pages 349-400
  4. Back Matter
    Pages 401-482

About this book

Introduction

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

Keywords

Brownian Motion Interacting Particle Systems Ito Calculus Levy Processes Stochastic Differential Equations Stochastic Processes

Authors and affiliations

  • Vincenzo Capasso
    • 1
  • David Bakstein
    • 2
  1. 1.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)Università degli Studi di MilanoMilanItaly
  2. 2.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)Università degli Studi di MilanoMilanItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-2757-9
  • Copyright Information Springer Science+Business Media New York 2015
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-2756-2
  • Online ISBN 978-1-4939-2757-9
  • Series Print ISSN 2164-3679
  • Series Online ISSN 2164-3725
  • Buy this book on publisher's site