Stochastic Systems: Uncertainty Quantification and Propagation

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

 

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Contents

1 Introduction
1
2 Essentials of Probability Theory
8
3 Random Functions
59
4 Stochastic Integrals
128
5 Its 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
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About the author (2012)

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.

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