An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology, and medicine

書誌事項

An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology, and medicine

Vincenzo Capasso, David Bakstein

(Modeling and simulation in science, engineering & technology)

Birkhäuser , Springer, c2015

3rd ed

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注記

Includes bibliographical references (p. 457-467) and index

内容説明・目次

内容説明

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

目次

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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詳細情報

  • NII書誌ID(NCID)
    BB19090134
  • ISBN
    • 9781493927562
  • LCCN
    2015938721
  • 出版国コード
    xx
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    [S.l.],New York
  • ページ数/冊数
    xvi, 482 p.
  • 大きさ
    25 cm
  • 親書誌ID
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