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＜電子ブック＞
An Introduction to Continuous-Time Stochastic Processes : Theory, Models, and Applications to Finance, Biology, and Medicine / by Vincenzo Capasso, David Bakstein
(Modeling and Simulation in Science, Engineering and Technology. ISSN:21643725)

版	3rd ed. 2015.
出版者	(New York, NY : Springer New York : Imprint: Birkhäuser)
出版年	2015
本文言語	英語
大きさ	XVI, 482 p. 14 illus : online resource
著者標目	*Capasso, Vincenzo author Bakstein, David author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical models LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Biomathematics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Probability Theory FREE:Mathematical Modeling and Industrial Mathematics FREE:Mathematics in Business, Economics and Finance FREE:Mathematical and Computational Biology FREE:Mathematical and Computational Engineering Applications
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-2757-9

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