Fixing the quadratic proxy in a sub-gamma bound at the true variance leaves a scale to optimize, and a two-sided infinitely divisible law generally requires different scales in the two directions. For a centered law with finite nonzero variance, we normalize its Kolmogorov canonical measure and multiply the resulting v...
A right sub-gamma bound is described by a quadratic proxy $v$ and a pole $c$, and the pair is not unique: enlarging either preserves it. Fixing $v$ at the variance $V$ removes the ambiguity at quadratic order but is a convention, not a consequence. For centered infinitely divisible laws with finite nonzero variance we...
Let X be a centered spectrally positive infinitely divisible random variable with finite nonzero variance V. We determine the smallest scale c in a right-sided sub-gamma bound whose quadratic proxy is fixed at V. A probability transform of the normalized Kolmogorov canonical measure produces a nonnegative variable R_X...
Let X be a centered infinitely divisible random vector with finite second moment and covariance matrix Sigma. We define the radial pole C_X(t) as the smallest scale in a right sub-gamma bound forwhose quadratic proxy is fixed at the true variance t^T Sigma t. A canonical directional measure and an independent Beta(1,2)...
Yi-Chuan Chen, Xin Wang· 1 citation· ⚡1
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