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DTIC ADA212612: Tightness of Synchronous Processes |
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by Defense Technical Information Center |
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Let X = (X(t) : t or = 0 be a positive recurrent |
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synchronous process (PRS), that is, a process for which |
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there exists an increasing sequence of random times |
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tau=(tau(k)) such that for each k the distribution of |
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theta sub tau(k) o X = X (t+tau(k)):t or = 0) is the same |
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and the cycle lengths (Tn = tau(n+1)-tau(n) have finite |
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first moment. Whereas the ergodic properties of such |
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processes are well known in the literature, the same is |
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not so for the distributional properties of either the |
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marginals X (t) or more generally the shifted processes |
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theta sub s X = X (s+t) : t or = 0) in function or space. |
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The present paper shows that these distributions are in |
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fact tight. In contrast to classical regenerative |
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processes the standard types of regularity assumptions |
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(non-lattice cycle length distribution, mixing) do not |
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ensure weak convergence to steady-state for a PRS. |
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Applications are given in the context of one- dependent |
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regenerative (od-R) processes. These arise in the |
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queueing models that motivated this paper. |
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Date Published: 2018-02-23 12:19:24 |
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Identifier: DTIC_ADA212612 |
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Item Size: 7571700 |
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Language: english |
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Media Type: texts |
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# Topics |
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DTIC Archive; Glynn, Peter; STANFORD ... |
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