Infinite divisibility of hitting times for symmetric stable processes
Let \(T_a\) be the first hitting time of a nonzero point \(a\) by a symmetric strictly \(\alpha\)-stable L\'evy process, where \(1<\alpha<2\). We give a computer-assisted classification of its ordinary additive infinite divisibility. There is a unique threshold \(\alpha_*\), with \(1.6670659903<\alpha_*<1.6670659915\), such that \(T_a\) is infinitely divisible if and only if \(1<\alpha\le\alpha_*\). The threshold is characterized by a unique zero contact of the canonical inverse logarithmic-derivative kernel. The proof combines explicit analytic estimates, rigorous interval covers, Gaussian…
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