Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators

Abstract: In this paper we present some extensions of recent noncentral moderate deviation results in the literature. In the first part we generalize the results in \cite{BeghinMacciSPL2022} by considering a general L\'evy process ${S(t):t\geq 0}$ instead of a compound Poisson process. In the second part we assume that ${S(t):t\geq 0}$ has bounded variation and is not a subordinator; thus ${S(t):t\geq 0}$ can be seen as the difference of two independent non-null subordinators. In this way we generalize the results in \cite{LeeMacci} for Skellam processes.