An Introduction to Continuous-Time Stochastic Processes

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

Vincenzo Capasso, David Bakstein (Autoren)

Buch | Hardcover

482 Seiten

2015 | 3rd ed. 2015
Birkhauser Boston Inc (Verlag)
978-1-4939-2756-2 (ISBN)

Infos

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

Autor

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).

Inhalt

Part I: Theory of Stochastic Processes.- Fundamentals of Probability.- Stochastic Processes.- The Itô Integral.- Stochastic Differential Equations.- Stability, Stationary, Ergodicity.- Part II: Applications of Stochastic Processes.- Applications to Finance and Insurance.- Applications to Biology and Medicine.- Measure and Integration.- Convergence of Probability Measures on Metric Spaces.- Appendices.

Produkt-Details

• Reihe/Serie: Modeling and Simulation in Science, Engineering and Technology
• Zusatzinfo: 4 Tables, black and white; 14 Illustrations, black and white; XVI, 482 p. 14 illus.
• Verlagsort: Secaucus
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 910 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: Brownian motion • Interacting Particle Systems • Ito Calculus • Levy processes • Stochastic differential equations • Stochastic Processes
• ISBN-10: 1-4939-2756-6 / 1493927566
• ISBN-13: 978-1-4939-2756-2 / 9781493927562
• Zustand: Neuware