A renewal version of the Sanov theorem. (English) Zbl 1307.60121

Mariani, Mauro; Zambotti, Lorenzo

Electron. Commun. Probab. 19, Paper No. 69, 13 p. (2014).

Summary: Large deviations for the local time of a process \(X_t\) are investigated, where \(X_t = x_i\) for \(t\in [S_{i-1},S_i[\) and \((x_j)\) are i.i.d. random variables on a Polish space, \(S_j\) is the \(j\)-th arrival time of a renewal process depending on \((x_j)\). No moment conditions are assumed on the arrival times of the renewal process.

MSC:

60K05	Renewal theory
60F10	Large deviations

Keywords:

renewal processes; large deviations; Sanov theorem; heavy tails