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Variational Principles for the Limiting Variance

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Book cover Fluctuations in Markov Processes

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 345))

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Abstract

The formulas for the limiting covariance matrix obtained for the class of diffusions considered in Chap. 9 are not explicit in terms of their coefficients. In this chapter we give upper and lower bounds for the quadratic form corresponding to the limiting covariance matrix. They are formulated in terms of variational principles and can be used to obtain further information about properties of the limiting normal law.

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Komorowski, T., Landim, C., Olla, S. (2012). Variational Principles for the Limiting Variance. In: Fluctuations in Markov Processes. Grundlehren der mathematischen Wissenschaften, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29880-6_10

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