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The Averaging Principle. Fluctuations in Dynamical Systems with Averaging

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL,volume 260)

Summary.

In Chap. 7, rapidly oscillating stochastic perturbations of dynamical systems are considered. Results of the law-of-large-numbers type, those of central-limit theorem type, and large-deviation results are obtained. Those last results are applied to the asymptotics of the behavior of the perturbed dynamical system on growing time intervals.

Keywords

  • Markov Process
  • Invariant Measure
  • Gaussian Process
  • Equilibrium Position
  • Stochastic Differential Equation

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Freidlin, M.I., Wentzell, A.D. (2012). The Averaging Principle. Fluctuations in Dynamical Systems with Averaging. In: Random Perturbations of Dynamical Systems. Grundlehren der mathematischen Wissenschaften, vol 260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25847-3_7

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