An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance, Biology, and Medicine (Modeling and Simulation in Science, Engineering and Technology) - Hardcover

Capasso, Vincenzo; Bakstein, David

Hardcover

ISBN 10: 1493927566 ISBN 13: 9781493927562

Publisher: Birkhäuser, 2015

Synopsis

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 this title

About the Author

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).

From the Back Cover

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

Edition details

• Publisher: Birkhäuser
• Publication date: 2015
• ISBN 10: 1493927566
• ISBN 13: 9781493927562
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 498