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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 epidemicsFinancial market models: the non-arbitrage principleContingent claim valuation modelsRisk analysis in insuranceAn 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.
List of contents
Preface.
- Part I: The Theory of Stochastic Processes.
- Fundamentals of Probability.
- Stochastic Processes.
- The Ito 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.
