Hitting Probabilities and Large Deviations
Let {Yn}n∈Z+ be a sequence of random variables in Rdand let$A \subset \mathbb{R}^d$. Then P{Yn∈ A for some n} is the hitting probability of the set A by the sequence {Yn}. We consider the asymptotic behavior, as m → ∞, of P{Yn∈ mA, some n} = P{hitting mA} whenever (1) the probability law of Yn/n sat...
Gespeichert in:
Veröffentlicht in: | The Annals of probability 1996-10, Vol.24 (4), p.2065-2078 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Let {Yn}n∈Z+
be a sequence of random variables in Rdand let$A \subset \mathbb{R}^d$. Then P{Yn∈ A for some n} is the hitting probability of the set A by the sequence {Yn}. We consider the asymptotic behavior, as m → ∞, of P{Yn∈ mA, some n} = P{hitting mA} whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set A. For a particular function Ĩ, we show P{Yn∈ mA, some n} ≈ exp(-mĨ(A)). |
---|---|
ISSN: | 0091-1798 2168-894X |
DOI: | 10.1214/aop/1041903218 |