An introduction to continuous-time stochastic processes: theory, models, and applications to finance, biology, and medicine / Vincenzo Capasso, David Bakstein

Auteur: Capasso, Vincenzo (1945-) - AuteurCo-auteur: Bakstein, David (1975-) - AuteurType de document: Livre numérique Collection: Modeling and simulation in science, engineering and technology Langue: anglaisÉditeur: Boston : Birkhäuser, 2005 ISBN: 9780817644284 Note: This is an introductory text on continuous time stochastic processes and their applications to finance and biology. The first part of the book reviews basic probability and then covers the basic continuous time processes such as Brownian motion, point processes, etc. It then introduces the Itô integral and Itô formula, and develops the basic theory of stochastic differential equations, inclusive of Lyapunov-type stability criteria. Proofs that are very technical are omitted. The second part of the book deals with applications. The chapter on finance and insurance covers option pricing, interest rate models and insurance risk. The chapter on biology and medicine considers a variety of models of population dynamics and an application to neurosciences. Four appendices cover the background from analysis required in the book, viz., measure and integration, probability measures on metric spaces, elliptic and parabolic p.d.e.'s, and stability theory for ordinary differential equations. The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. (MathScinet) Sujets MSC: 60-01 Probability theory and stochastic processes -- Instructional exposition (textbooks, tutorial papers, etc.)
60Gxx Probability theory and stochastic processes -- Stochastic processes
60H05 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic integrals
60H10 Probability theory and stochastic processes -- Stochastic analysis -- Stochastic ordinary differential equations
60H30 Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.)
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This is an introductory text on continuous time stochastic processes and their applications to finance and biology. The first part of the book reviews basic probability and then covers the basic continuous time processes such as Brownian motion, point processes, etc. It then introduces the Itô integral and Itô formula, and develops the basic theory of stochastic differential equations, inclusive of Lyapunov-type stability criteria. Proofs that are very technical are omitted.
The second part of the book deals with applications. The chapter on finance and insurance covers option pricing, interest rate models and insurance risk. The chapter on biology and medicine considers a variety of models of population dynamics and an application to neurosciences.
Four appendices cover the background from analysis required in the book, viz., measure and integration, probability measures on metric spaces, elliptic and parabolic p.d.e.'s, and stability theory for ordinary differential equations.
The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. (MathScinet)

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