Stochastic Systems - Uncertainty Quantification and Propagation

Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents:
A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis

Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences

Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions

Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners.

List of contents

Probability Essentials.- Random Functions.- Probabilistic Models.- Stochastic Integrals and Itô's Formula.- Properties of Solutions of Stochastic Equations.- Stochastic Equations with Small Uncertainty.- Stochastic Algebraic Equations.- Stochastic Differential Equations with Deterministic Coefficients.- Stochastic Differential Equations with Random Coefficients.

About the author

Mircea Grigoriu is a professor at Cornell University whose research has focused primarily on applications of to applied sciences and engineering. His contributions to probabilistic models for actions and physical properties, random vibration, stochastic mechanics, system reliability, and Monte Carlo simulation are reported in over 200 technical papers, three books, and this new book on Stochastic Systems. His work has been recognized by numerous prizes, for example, the 2002 Alfred Freudenthal Medal, the election to the Romanian Academy of Technical Sciences in 2004, and the 2005 Norman Medal.

Summary

This book offers accurate, efficient methods for solving stochastic equations, with a focus on formulating equations that apply to problems in engineering and applied sciences. Numerous examples illustrate essential theoretical concepts, models and methods.

Additional text

From the reviews:
“Monograph provides a broad overview over the power of stochastic systems on a high mathematical level. It is aimed at interested readers from various fields of science and practitioners … . provides the mathematical understanding to a broad spectrum of systems subject to randomness and a wast repertoire of techniques to tackle these phenomena. … great source for practitioners and scientists of various fields and will equip the reader with the knowledge to properly formulate his models and to derive the understanding of their behavior.” (Jan Gairing, Zentralblatt MATH, Vol. 1247, 2012)
“The book deals with theoretical and computational aspects of stochastic equations. … The book is self-contained and can be used for teaching graduate courses. … Each chapter has illustrative examples and end of chapter problems which are useful for preparing a graduate course or for readers who will use this book for self-education.” (Mikhail V. Tretyakov, Mathematical Reviews, January, 2013)

Report

From the reviews:
"Monograph provides a broad overview over the power of stochastic systems on a high mathematical level. It is aimed at interested readers from various fields of science and practitioners ... . provides the mathematical understanding to a broad spectrum of systems subject to randomness and a wast repertoire of techniques to tackle these phenomena. ... great source for practitioners and scientists of various fields and will equip the reader with the knowledge to properly formulate his models and to derive the understanding of their behavior." (Jan Gairing, Zentralblatt MATH, Vol. 1247, 2012)
"The book deals with theoretical and computational aspects of stochastic equations. ... The book is self-contained and can be used for teaching graduate courses. ... Each chapter has illustrative examples and end of chapter problems which are useful for preparing a graduate course or for readers who will use this book for self-education." (Mikhail V. Tretyakov, Mathematical Reviews, January, 2013)

Product details

• Authors: Mircea Grigoriu
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.05.2012
• EAN: 9781447123262
• ISBN: 978-1-4471-2326-2
• No. of pages: 532
• Weight: 940 g
• Illustrations: XII, 532 p.
• Series: Springer Series in Reliability Engineering; Springer Series in Reliability Engineering; Springer Series in Realibility Engineering
• Subject: Natural sciences, medicine, IT, technology > Physics, astronomy