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

Format:

Book

Author/Creator:

Capasso, Vincenzo, 1945- author.

Bakstein, David, 1975- author.

Series:

Modeling and Simulation in Science, Engineering and Technology, 2164-3725

Language:

English

Subjects (All):

Stochastic processes.

Stochastic models.

Mathematical models.

Social sciences--Mathematics.

Social sciences.

Biomathematics.

Stochastic Processes.

Stochastic Modelling.

Mathematical Modeling and Industrial Mathematics.

Mathematics in Business, Economics and Finance.

Mathematical and Computational Biology.

Local Subjects:

Stochastic Processes.

Stochastic Modelling.

Mathematical Modeling and Industrial Mathematics.

Mathematics in Business, Economics and Finance.

Mathematical and Computational Biology.

Physical Description:

1 online resource (574 pages)

Edition:

4th ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2021.

Summary:

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.

Contents:

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.

ISBN:

3-030-69653-7

OCLC:

1263871452