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capasso vincenzo; bakstein david - an introduction to continuous-time stochastic processes

An Introduction to Continuous-Time Stochastic Processes Theory, Models, and Applications to Finance, Biology, and Medicine

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 06/2022
Edizione: 4th ed. 2021





Trama

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it 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. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di?erent ?elds.

Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic di?erential equations.

An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. 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. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.





Sommario

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.




Autore

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).










Altre Informazioni

ISBN:

9783030696559

Condizione: Nuovo
Collana: Modeling and Simulation in Science, Engineering and Technology
Dimensioni: 235 x 155 mm
Formato: Brossura
Illustration Notes:XXI, 560 p. 15 illus., 1 illus. in color.
Pagine Arabe: 560
Pagine Romane: xxi


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