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Record Nr. |
UNINA9910299761203321 |
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Autore |
Capasso Vincenzo |
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Titolo |
An Introduction to Continuous-Time Stochastic Processes : Theory, Models, and Applications to Finance, Biology, and Medicine / / by Vincenzo Capasso, David Bakstein |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Birkhäuser, , 2015 |
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ISBN |
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Edizione |
[3rd ed. 2015.] |
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Descrizione fisica |
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1 online resource (XVI, 482 p. 14 illus.) |
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Collana |
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Modeling and Simulation in Science, Engineering and Technology, , 2164-3725 |
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Disciplina |
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Soggetti |
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Probabilities |
Mathematical models |
Social sciences - Mathematics |
Biomathematics |
Engineering mathematics |
Engineering - Data processing |
Probability Theory |
Mathematical Modeling and Industrial Mathematics |
Mathematics in Business, Economics and Finance |
Mathematical and Computational Biology |
Mathematical and Computational Engineering Applications |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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