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An Introduction to Continuous-time Stochastic Processes
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An Introduction to Continuous-time Stochastic Processes

An Introduction to Continuous-time Stochastic Processes

Theory, Models, and Applications to Finance, Biology, and Medicine

Vincenzo Capasso, David Bakstein - Collection Modeling and Simulation Science, Engineering and Technology

343 pages, parution le 14/02/2005

Résumé

This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Key topics covered include:

  • Interacting particles and agent-based models (ant colonies)
  • Population dynamics: from birth and death processes to epidemics
  • Financial market models: the non-arbitrage principle
  • Contingent claim valuation models
  • Risk analysis in insurance

An Introduction to Continuous-Time Stochastic Processes will be of interest to a broad audience of students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, biotechnology, physics, and engineering. Suitable as a textbook for graduate or advanced undergraduate courses, 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.

Sommaire

  • The Theory of Stochastic Processes
    • Fundamentals of Probability
    • Stochastic Processes
    • The Itô Integral
    • Stochastic Differential Equations
  • The Applications of Stochastic Processes
    • Applications to Finance and Insurance
    • Applications to Biology and Medicine
  • Appendices
    • A: Measure and Integration
    • B: Convergence of Probability Measures on Metric Spaces
    • C: Maximum Principles of Elliptic and Parabolic Operators
    • D: Stability of Ordinary Differential Equations
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Vincenzo Capasso, David Bakstein
Collection Modeling and Simulation Science, Engineering and Technology
Parution 14/02/2005
Nb. de pages 343
Format 16 x 24
Couverture Relié
Poids 628g
Intérieur Noir et Blanc
EAN13 9780817632342
ISBN13 978-0-8176-3234-2

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