Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes (Q1805772)

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scientific article; zbMATH DE number 1364484
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Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes
scientific article; zbMATH DE number 1364484

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    Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes (English)
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    18 November 1999
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    Let \(\{X(t)\), \(t\in [0,1]\}\) be a complex-valued strongly stationary harmonizable \(\xi_g\)-radial process. The authors study stationary harmonizable infinitely divisible processes of the form \(Y(t)=\hbox {Re}\{X(t)\}\). Let \(N_u(0,1)\) be the number of crossings of a level \(u\) by \(Y(t)\) on \([0,1]\). Equivalent upper and lower bounds for \(EN_0(0,1)\) are derived and cruder bounds are presented for \(EN_u(0,1)\) for an arbitrary level \(u\). A limit for \(EN_u(0,1)\) is given as \(u\to \infty \).
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    harmonizable infinitely divisible process
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    Lévy measure
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    Rice's formula
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    regularly varying functions
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    independent increment
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    stable process
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