Stochastic Systems: Uncertainty Quantification and Propagation

Mircea Grigoriu

Springer Science & Business Media, May 15, 2012 - Technology & Engineering - 532 pages

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.

Contents

• 1 Introduction: 1
• 2 Essentials of Probability Theory: 8
• 3 Random Functions: 59
• 4 Stochastic Integrals: 128
• 5 Itôs Formula and Applications: 155
• 6 Probabilistic Models: 201
• 7 Stochastic Ordinary Differential and Difference Equations: 237
• 8 Stochastic Algebraic Equations: 336
• 9 Stochastic Partial Differential Equations: 379
• A Parametric Models Quantizers and Stochastic Reduced Order Models: 455

About the author

Mircea Grigoriu is a professor at Cornell University whose research has focused primarily on applications of probability theory 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.

Bibliographic information

• Title: Stochastic Systems: Uncertainty Quantification and Propagation; Springer Series in Reliability Engineering
• Author: Mircea Grigoriu
• Edition: illustrated
• Publisher: Springer Science & Business Media, 2012
• ISBN: 1447123271, 9781447123279
• Length: 532 pages
• Subjects: Mathematics / Applied; Mathematics / Probability & Statistics / General; Technology & Engineering / Engineering (General); Technology & Engineering / Manufacturing; Technology & Engineering / Quality Control