Titlebook: Random Perturbation Methods with Applications in Science and Engineering; Anatoli V. Skorokhod,Frank C. Hoppensteadt,Habib S Book 2002 Spr

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Averaging,ow the limit as . → 0 of the perturbed problem is related to the averaged problem .(.(·)) = 0. The results in this chapter show how to derive, under natural conditions, convergence properties of ..(., .) - .(t) as . → 0. In general, this error will approach zero in a probabilistic sense that is made precise in each case.

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Ergodic Theorems,s plausible that a collection of gas molecules in a confined volume will move in such a way that they will hit any sub-volume a proportion of time comparable to the size of the sub-volume. It was proposed by Boltzmann in the “ergodic surmise” that time averages and space averages agree in this sense

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CARK

Normal Deviations,ce between them. In this chapter we consider the remainder ..(.) - x?(.) in greater detail. We refer to this remainder as the first-order deviation, or simply the .. The deviation tends to zero in some sense if an averaging theorem is true. When that is the case, we can investigate the asymptotic be

Ingenuity

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譏諷

Markov Chains with Random Transition Probabilities,totic behavior of the chain and its transition probabilities as . → ∞ under the assumption that the transition probabilities of the Markov chain are close to those of a homogeneous Markov chain having nonrandom transition probabilities.

Palter

Randomly Perturbed Mechanical Systems,hrough a local maximum of the potential energy, the system can pass through a saddle-saddle connection and go from having two possible oscillations to having only one. On the other hand, when dissipation is present, local minima of the potential function become stable equilibria. For example, in the