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An introduction to continuous-time s...

Bakstein, David.

An introduction to continuous-time stochastic processestheory, models, and applications to finance, biology, and medicine /

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to continuous-time stochastic processesby Vincenzo Capasso, David Bakstein.
Reminder of title:	theory, models, and applications to finance, biology, and medicine /
Author:	Capasso, Vincenzo.
other author:	Bakstein, David.
Published:	Cham :Springer International Publishing :2021.
Description:	xxi, 560 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes.
Online resource:	https://doi.org/10.1007/978-3-030-69653-5
ISBN:	9783030696535$q(electronic bk.)

An introduction to continuous-time stochastic processestheory, 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. - Fourth edition. - Cham :Springer International Publishing :2021. - xxi, 560 p. :ill., digital ;24 cm. - Modeling and simulation in science, engineering and technology,2164-3679. - 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 Ito 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 Ito 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$q(electronic bk.)

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

181874
Stochastic processes.

LC Class. No.: QA274 / .C373 2021

Dewey Class. No.: 519.23

An introduction to continuous-time stochastic processestheory, models, and applications to finance, biology, and medicine /
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505 0 $a 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 Ito 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.
520 $a 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 Ito 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.
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