An introduction to continuous-time stochastic processes theory, models, and applications to finance, biology, and medicine / [electronic resource] :

• 作者： Capasso, Vincenzo.
• 其他作者：
  • Bakstein, David.
  • SpringerLink (Online service)
• 其他題名：
  • Modeling and simulation in science, engineering and technology
• 出版： New York, NY : Springer New York :Imprint: Birkhauser
• 版本：3rd ed.
• 叢書名： Modeling and simulation in science, engineering and technology
• 主題： Stochastic processes , Stochastic processes--Mathematical models , Mathematics , Probability Theory and Stochastic Processes. , Mathematical Modeling and Industrial Mathematics. , Quantitative Finance. , Mathematical and Computational Biology. , Appl.Mathematics/Computational Methods of Engineering.
• ISBN： 9781493927579 (electronic bk.) 、 9781493927562 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Part I: Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Ito 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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• 摘要註: 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 un
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