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Variance Calculation through Large Deviation Techniques

Abstract : In this paper, we show how to use the expression of entropy in order to calculate variances. Three cases are analyzed: independent and identically distributed (iid) variables, Markov chains (in discrete time) and jump Markov processes (in continuous time). This framework is valid far beyond these case studies, e.g. in transportation and telecommunication networks and likely in all models where the entropy is explicit. The method allows to derive the variance from the entropy function, which is a classical quantity in large deviations. Moreover, the entropy has often a rather simple expression (e.g. for networks). Here we show a closed formula expressing the variance in terms of derivatives of the entropy; by-products are also obtained, such as martingales, used in the proof of the central limit theorem. These results might be a good starting point for further developments, e.g. calculation of exact asymptotics (instead of logarithmic ones in large deviation) or solving entropy minimization problems.
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Submitted on : Tuesday, May 23, 2006 - 7:54:28 PM
Last modification on : Friday, February 4, 2022 - 3:09:56 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:55:31 PM


  • HAL Id : inria-00072147, version 1



Arnaud de la Fortelle. Variance Calculation through Large Deviation Techniques. [Research Report] RR-4441, INRIA. 2002. ⟨inria-00072147⟩



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