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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	An Introduction to Continuous-Time Stochastic Processes/ by Vincenzo Capasso, David Bakstein.
其他題名:	Theory, Models, and Applications to Finance, Biology, and Medicine /
作者:	Capasso, Vincenzo.
其他作者:	Bakstein, David.
面頁冊數:	XXI, 560 p. 15 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical and Computational Biology. -
電子資源:	https://doi.org/10.1007/978-3-030-69653-5
ISBN:	9783030696535

An Introduction to Continuous-Time Stochastic Processes = Theory, Models, and Applications to Finance, Biology, and Medicine /
Capasso, Vincenzo.

An Introduction to Continuous-Time Stochastic ProcessesTheory, Models, and Applications to Finance, Biology, and Medicine /[electronic resource] :by Vincenzo Capasso, David Bakstein. - 4th ed. 2021. - XXI, 560 p. 15 illus., 1 illus. in color.online resource. - Modeling and Simulation in Science, Engineering and Technology,2164-3725. - Modeling and Simulation in Science, Engineering and Technology,.

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.

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, particularly the applications explored in the second half of the book.

ISBN: 9783030696535

Standard No.: 10.1007/978-3-030-69653-5doiSubjects--Topical Terms:

786706
Mathematical and Computational Biology.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

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