Exponential Asymptotics and Law of the Iterated Logarithm for Intersection Local times of Random Walks1 by Xia Chen
نویسنده
چکیده
with the right-hand side being identified in terms of the the best constant of the Gagliardo–Nirenberg inequality. Within the scale of moderate deviations, we also establish the precise tail asymptotics for the intersection local time In = #{(k1, . . . , kp) ∈ [1, n];S1(k1)= · · · = Sp(kp)} run by the independent, symmetric, Zd -valued random walks S1(n), . . . , Sp(n). Our results apply to the law of the iterated logarithm. Our approach is based on Feynman–Kac type large deviation, time exponentiation, moment computation and some technologies along the lines of probability in Banach space. As an interesting coproduct, we obtain the inequality ( EI n1+···+na )1/p ≤ ∑ k1+···+ka=m k1 ,...,ka≥0 m! k1! · · ·ka ! ( EI k1 n1 )1/p · · · (EIka na )1/p
منابع مشابه
Moderate Deviations and Law of the Iterated Logarithm for Intersections of the Ranges of Random Walks1 By
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