Sample path large deviations for Lévy processes and random walks with Weibull increments. (English) Zbl 1477.60051
The current paper focuses on extended large deviations principles (LDP) for Lévy processes and random walks with heavy-tailed step size distribution. The authors prove an extended LDP in the \(\mathbb{J}_1\) topology for a suitable rate function for the processes under consideration. Their approach is based on a decomposition of the processes into the contribution arising from the \(k\) largest jumps in a Poisson process, and the remainder. The results are optimal and have several applications. In particular, one can apply the results in order to extend the classical Donsker-Varadhan LDP for unbounded functionals of Markov chains.
Reviewer: Ecaterina Sava-Huss (Innsbruck)
MSC:
| 60F10 | Large deviations |
| 60G17 | Sample path properties |
| 60G50 | Sums of independent random variables; random walks |
| 60G51 | Processes with independent increments; Lévy processes |
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