An Introduction to Continuous-Time Stochastic Processes [electronic resource] : Theory, Models, and Applications to Finance, Biology, and Medicine / by Vincenzo Capasso, David Bakstein
Imprint
Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2012
From reviewsย of First Edition: The book isย ... an account of fundamental concepts as they appear in relevant modern applications and literature.ย ... 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. โZentralblatt 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. โMathematical Reviews Revised and enhanced, this conciselyย written second edition of An Introduction to Continuous-Time Stochastic Processes is a rigorousย and self-contained introduction to the theoryย of continuous-time stochastic processes, stochasticย integrals,ย and stochastic differentialย 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 topicsย 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 toย finance and biology, including stable laws, Lรฉvy processes, and Itรด-Lรฉvy calculus *ย Supplemental appendix to provideย basic facts on semigroups of linear operators An Introduction to Continuous-Time Stochastic Processes, Second Editionย will be of interest to a broad audience of students, pure and applied mathematicians, and researchersย and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduateย courses, as well asย European Masters courses (according toย the two-year-long second cycle of the "Bologna Scheme"),ย 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
CONTENT
Part I. The Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itรด Integral -- Stochastic Differential Equations -- Part II. The Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine -- Part III. Appendices -- Measure and Integration -- Convergence of Probability Measures on Metric Spaces -- Elliptic and Parabolic Operators -- D Semigroups and Linear Operators.-ย E Stability of Ordinary Differential Equations -- References
SUBJECT
Mathematics
Finance
Distribution (Probability theory)
Engineering mathematics
Mathematics
Probability Theory and Stochastic Processes
Mathematical Modeling and Industrial Mathematics
Quantitative Finance
Mathematical and Computational Biology
Applications of Mathematics
Appl.Mathematics/Computational Methods of Engineering
