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- W2018468534 abstract "Let (Xn)n⩾1 be a sequence of real random variables. The local score is Hn=max1⩽i<j⩽n(Xi+⋯+Xj). If (Xn)n⩾1 is a “good” Markov chain under its invariant measure, the Xi are centered, we prove that Hn/n converges in distribution to B1∗ when n→+∞, where B1∗=max0⩽u⩽1|Bu| and (Bu,u⩾0) is a standard Brownian motion, B0=0. If (Xn)n⩾1 a sequence of i.i.d. random variables, E(X1)=δ/n and Var(X1)=σ2>0, we prove the convergence of Hn/n to σξδ/σ where ξγ=max0⩽u⩽1{(B(u)+γu)−min0⩽s⩽u(B(s)+γs)}. We approximate the probability distribution function of ξγ and we determine the asymptotic behavior of P(ξγ⩾a),a→+∞." @default.
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- W2018468534 date "2003-09-01" @default.
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- W2018468534 title "Asymptotic behavior of the local score of independent and identically distributed random sequences" @default.
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- W2018468534 doi "https://doi.org/10.1016/s0304-4149(03)00061-9" @default.
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