Abstract
Examples are used to introduce deterministic and stochastic equations and demonstrate the need to describe the state of physical systems by using stochastic equations. While the focus in mathematical studies of stochastic equations is primarily on technical aspects related to the existence and uniqueness of the solutions, the focus in applied studies is on the calculations of these solutions. Graduate courses based on material presented in the book can concentrate on the formulation of stochastic problems, random vibration by Itô’s calculus, and stochastic partial differential equations with applications to random heterogeneous materials.
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Acknowledgments
This book could not have been completed without the contributions of many individuals. In particular, I wish to express my deepest appreciation to Professors S. I. Resnick and G. Samorodnitsky of Cornell University, Professor F. Potra of the University of Maryland Baltimore County, and Professor S. T. Ariaratnam of the University of Waterloo, Canada, for numerous technical discussions, Dr. E. Simiu of National Institute of Standards and Technology for reviewing the entire manuscript, Professors W. Aquino and C. Earls for useful comments on Chap. 9, my doctoral student S. Saroukhani for helping with some numerical examples, Mr. C. Willkens for his enthusiastic and professional support of the computer hardware and software used in this project, and my son Bogdan for his help with figures, index, and other aspects of the book. Finally, I am grateful to my wife Betsy for understanding, encouragement, support, as well as most valuable comments to this chapter.
A significant part of the work incorporated in this book has been supported by the National Science Foundation, Sandia National Laboratories, National Institute of Standards and Technology, Jet Propulsion Laboratory, Air Force Office of Scientific Research, Federal Aviation Administration, and other institutions. I am indebted to these organizations and their continued support.
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Grigoriu, M. (2012). Introduction. In: Stochastic Systems. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2327-9_1
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DOI: https://doi.org/10.1007/978-1-4471-2327-9_1
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