An Introduction to Continuous-Time Stochastic Processes: Theory, Models, and Applications to Finance,...

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Vincenzo Capasso David Bakstein

An Introduction to Continuous-Time Stochastic Processes

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

Vincenzo Capasso, David Bakstein

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English

Springer Nature Switzerland AG
20 June 2022

Probability & statistics; Mathematical modelling; Stochastics; Maths for scientists

Series: Modeling and Simulation in Science, Engineering and Technology

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 diﬀerent ﬁelds. 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 diﬀerential 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.

By: Vincenzo Capasso, David Bakstein
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 4th ed. 2021
Dimensions: Height: 235mm, Width: 155mm,
Weight: 884g
ISBN: 9783030696559
ISBN 10: 3030696553
Series: Modeling and Simulation in Science, Engineering and Technology
Pages: 560
Publication Date: 20 June 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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).

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

“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)