Ultrafast Subordinators and Their Hitting Times

Mihály Kovács; Mark M. Meerschaert

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This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation $x^{'''} + q (t) x^{- γ} = 0$ , by means of regularly varying functions, where $γ$ is a positive constant and $q$ is a positive continuous function on $[a, \infty)$ . It is shown that if $q$ is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to $0$ as $t \to \infty$ and...