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Abstract: The extremal tail probabilities of moving sums in a marked Poisson randomfield is examined here. These sums are computed by adding up the weightedoccurrences of events lying within a scanning set of fixed shape and size.Change of measure and analysis of local random fields are used to provide tailprobabilities. The asymptotic constants are initially expressed in a form thatseems hard to evaluate and do not seem to provide any additional information onthe properties of the constants. A more sophisticated approach is thenundertaken giving rise to an expression that is not only neater but also ableto provide computable bounds. The technique used to obtain this constant canalso be modified to work on continuous processes.



Autor: Hock Peng Chan

Fuente: https://arxiv.org/







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