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Stochastic Systems pp 237–335Cite as

Stochastic Ordinary Differential and Difference Equations

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Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

Abstract

Summary Methods are developed for solving ordinary differential and difference equations with random coefficients and/or input. Following an introductory section (Sect. 1), we present methods for solving equations with deterministic coefficients and random input (Sect. 2), finite difference equations with random coefficients of arbitrary and small uncertainty (Sect. 3), and ordinary differential equations with random coefficients of arbitrary and small uncertainty (Sect. 4). The methods include Monte Carlo simulation, conditional analysis, stochastic reduced order models, stochastic Galerkin, stochastic collocation, Taylor series, and Neumann series. Applications from stochastic stability, noise induced transitions, random vibration, and reliability of degrading systems conclude the chapter (Sect. 5).

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Authors and Affiliations

  1. Hollister Hall, Cornell University, 14853, Ithaca, NY, USA

    Mircea Grigoriu

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  1. Mircea Grigoriu
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Grigoriu, M. (2012). Stochastic Ordinary Differential and Difference Equations. In: Stochastic Systems. Springer Series in Reliability Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-2327-9_7

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  • DOI: https://doi.org/10.1007/978-1-4471-2327-9_7

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  • Print ISBN: 978-1-4471-2326-2

  • Online ISBN: 978-1-4471-2327-9

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