In this paper we consider a suitable $\mathbb R^d$-valued process $(Z_t)$ and a
suitable family of nonempty subsets $(A(b):b>0)$ of $\mathbb R^d$ which, in some
sense, decrease to empty set as $b\rightarrow \infty$. In general let $T_b$ be the first
hitting time of $A(b)$ for the process $(Z_t)$. The main result relates
the large deviations principle of $(\frac{T_b}{b})$ as $b\rightarrow \infty$ with a large
deviations principle concerning $(Z_t)$ which agrees with a generalized
version of Mogulskii Theorem. The proof has some analogies with the proof
presented in \cite{DW} for a similar result concerning nondecreasing
univariate processes and their inverses with general scaling function.
Publié le : 2003-09-14
Classification:
large deviations,
first passage time,
Mogulskii Theorem,
homogeneous function of degree 1,
60F10
@article{1063372344,
author = {Macci, Claudio},
title = {Large deviations for hitting times of some decreasing sets},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {10},
number = {1},
year = {2003},
pages = { 379-390},
language = {en},
url = {http://dml.mathdoc.fr/item/1063372344}
}
Macci, Claudio. Large deviations for hitting times of some decreasing sets. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp. 379-390. http://gdmltest.u-ga.fr/item/1063372344/