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

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 Lévy process $\{S(t):t\ge 0\}$ instead of a compound Poisson process. In the second part we assume that $\{S(t):t\ge 0\}$ has bounded variation and is not a subordinator; thus $\{S(t):t\ge 0\}$ 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.