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The first-order asymptotic of waiting times with distortion between stationary processes

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1 Author(s)
Zhiyi Chi ; Dept. of Stat., Chicago Univ., IL, USA

Let X and Y be two independent stationary processes on general metric spaces, with distributions P and Q, respectively. The first-order asymptotic of the waiting time Wn(D) between X and Y, allowing distortion, is established in the presence of one-sided ψ-mixing conditions for Y. With probability one, n-1log W n(D) has the same limit as -n-1logQ(B(X1n, D)), where Q(B(X1 n, D)) is the Q-measure of the D-ball around (X1 ,...,Xn), with respect to a given distortion measure. Large deviations techniques are used to get the convergence of -n-1 log Q(B(X1n, D)). First, a sequence of functions Rn in terms of the marginal distributions of X1n and Y1n as well as D are constructed and demonstrated to converge to a function R(P, Q, D). The functions Rn and R(P, Q, D) are different from rate distortion functions. Then -n-1logQ(B(X1n , D)) is shown to converge to R(P, Q, D) with probability one

Published in:

IEEE Transactions on Information Theory  (Volume:47 ,  Issue: 1 )