HITTING PROBABILITIES AND LARGE DEVIATIONS † by Jeffrey F
نویسنده
چکیده
Let {Yn}n∈Z+ be a sequence of random variables in R and let A ⊂ R. 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} ≈ e−mĨ(A).
منابع مشابه
Hitting probabilities and large deviations
Let Ynn∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then PYn ∈ A for some n is the hitting probability of the set A by the sequence Yn. We consider the asymptotic behavior, as m → ∞, of PYn ∈ mA; some n = Phitting 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 ...
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