Vincenzo Capasso, David Bakstein

An Introduction to Continuous-Time Stochastic Processes (eBook, PDF)

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

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel AG
• Seitenzahl: 344
• Erscheinungstermin: 3. Januar 2008
• Englisch
• ISBN-13: 9780817644284
• Artikelnr.: 43729854

Autorenporträt

Vincenzo Capasso is a Professor of Probability and Mathematical Statistics at the University of Milan, an elected  member of the International Statistics Institute, a Fellow of The Institute of Mathematics and its Applications - UK, Past President of ECMI (the European Consortium for  Mathematics in Industry), and Past President of ESMTB (European Society for Mathematical and Theoretical Biology). David Bakstein has been working in the financial industry for close to 25 years, many of those dedicated to applied mathematical models. He originally studied and taught at both the LSE and University of Oxford (OCIAM & Lady Margaret Hall).

Inhaltsangabe

Foreword.- Preface to the Fourth Edition.- Preface to the Third Edition.- Preface to the Second Edition.- Preface.- Part I: Theory of Stochastic Processes.- Fundamentals of Probability.- Stochastic Processes.- The Itô 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.- Diffusion Approximation of a Langevin System.- Elliptic and Parabolic Equations.- Semigroups of Linear Operators.- Stability of Ordinary Differential Equations.- References.- Nomenclature.- Index.

Rezensionen

"Exercises are provided at the end of each chapter; the difficulty ranges from basic applications to more advanced ideas ... . Overall this book is a nice way to get into the basics of stochastic processes for someone working in a different field. It is quite reasonable that this could serve as either a main textbook or secondary reference for a graduate course. Sufficient details on each topic are provided by the authors, which makes this possible." (Eric Stachura, MAA Reviews, January 30, 2022)