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Birkhäuser - Birkhäuser Mathematics | An Introduction to Continuous-Time Stochastic Processes - Theory, Models, and Applications to

An Introduction to Continuous-Time Stochastic Processes

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

Capasso, Vincenzo, Bakstein, David

2005, XI, 343p. 13 illus..

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  • A rigorous and self-contained introduction to the theory of continuous-time stochastic processes
  • Concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods
  • Exercises at the end of each chapter; no previous knowledge of stochastic processes is required

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, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Key topics covered include:

* Interacting particles and agent-based models: from polymers to ants

* Population dynamics: from birth and death processes to epidemics

* Financial market models: the non-arbitrage principle

* Contingent claim valuation models: the risk-neutral valuation theory

* 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, 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.

Content Level » Research

Keywords » Measure - continuous-time stochastic process - linear optimization - model - modeling - operator - stability - stochastic process

Related subjects » Birkhäuser Applied Probability and Statistics - Birkhäuser Engineering - Birkhäuser Mathematics

Table of contents 

Preface Part I. The Theory of Stochastic Processes Fundamentals of Probability Stochastic Processes The Itô Integral Stochastic Differential Equations Part II. The Applications of Stochastic Processes Applications to Finance and Insurance Applications to Biology and Medicine Part III. 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 References

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