Abstract:We propose a definition of directional multivariate subexponential and convolution equivalent densities and find a useful characterization of these notions for a class of integrable and almost radial decreasing functions. We apply this result to show that the density of the absolutely continuous part of the compound Poisson measure built on a given density f is directionally convolution equivalent and inherits its asymptotic behaviour from f if and only if f is directionally convolution equivalent. We also ext… Show more
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