Author	Capasso, Vincenzo. author
Title	An Introduction to Continuous-Time Stochastic Processes [electronic resource] : Theory, Models, and Applications to Finance, Biology, and Medicine / by Vincenzo Capasso, David Bakstein
Imprint	New York, NY : Springer New York : Imprint: Birkhäuser, 2015
Edition	3rd ed. 2015
Connect to	http://dx.doi.org/10.1007/978-1-4939-2757-9
Descript	XVI, 482 p. 14 illus. online resource

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

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

1. Mathematics
2. Economics
3. Mathematical
4. Mathematical models
5. Probabilities
6. Biomathematics
7. Applied mathematics
8. Engineering mathematics
9. Mathematics
10. Probability Theory and Stochastic Processes
11. Mathematical Modeling and Industrial Mathematics
12. Quantitative Finance
13. Mathematical and Computational Biology
14. Appl.Mathematics/Computational Methods of Engineering