Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators
Pub. online: 31 December 2024
Type: Research Article
Open Access
Open Access
Received
7 August 2024
7 August 2024
Revised
16 December 2024
16 December 2024
Accepted
17 December 2024
17 December 2024
Published
31 December 2024
31 December 2024
Abstract
This paper presents some extensions of recent noncentral moderate deviation results. In the first part, the results in [Statist. Probab. Lett. 185, Paper No. 109424, 8 pp. (2022)] are generalized by considering a general Lévy process $\{S(t):t\ge 0\}$ instead of a compound Poisson process. In the second part, it is assumed 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 nonnull subordinators. In this way, the results in [Mod. Stoch. Theory Appl. 11, 43–61] for Skellam processes are generalized.
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