Probabilities of very large deviations

Hitting probabilities and large deviations

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: 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 ...

2078 Hitting Probabilities and Large Deviations

HITTING PROBABILITIES AND LARGE DEVIATIONS † by Jeffrey F

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. ...

2078 HITTING PROBABILITIES AND LARGE DEVIATIONS 1 By Jeffrey

HITTING PROBABILITIES AND LARGE DEVIATIONS 1 By Jeffrey