Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable

Tail Behavior of Stopped Lévy Processes With Markov Modulation

“…The arguments given in [16] were adapted to arbitrary d ∈ N by Nakagawa [20]. See, in particular, Theorem 5* therein, and see also [18,19,21] for closely related results. Explicit sharp bounds for the limits inferior and superior in (1.2) are provided in [16,20], but these are complicated in form for general d and are not required for the present discussion.…”