منابع مشابه
Moderate Deviations for Bounded Subsequences
Let (Xn)n≥1 be a sequence of random variables on a probability space (Ω, ,P) and p ≥ 1 a fixed real number. We say that (Xn)n≥1 is Lp-bounded if it has finite pth moments, that is, ‖Xn‖p ≤ C for some C > 0 and any n ≥ 1. Let ε > 0; finding the rate of convergence of the moderate deviations probabilities P[|∑k=1Xk| > εan] with an = (n logn)1/2 or (n loglogn)1/2 is known in the literature as Davi...
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We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.
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In this paper we are concerned with the moderate deviation principle for the normalized partial sums process Wn, considered as an element of D([0, 1]) (functions on [0, 1] with left-hand limits and continuous from the right), equipped with the Skorohod topology (see Section 14 in Billingsley (1968) for the description of the topology on D([0, 1])). More exactly, we say that the family of random...
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We consider a one-dimensional translation invariant point process of density one with uniformly bounded variance of the number NI of particles in any interval I . Despite this suppression of fluctuations we obtain a large deviation principle with rate function F(ρ) ' −L log Prob(ρ) for observing a macroscopic density profile ρ(x), x ∈ [0, 1], corresponding to the coarse-grained and rescaled den...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90097-r