Asymptotically invariant sampling and averaging from stationary-like processes

Olav Kallenberg

Stochastic Processes and their Applications, 1999, vol. 82, issue 2, 195-204

Abstract: Given a process X on or , we may form a random sequence [xi]1,[xi]2,... by sampling from X at some independent points [tau]1,[tau]2,... . If X is stationary up to shifts (which holds for broad classes of Markov and Palm processes) and the distribution of ([tau]n) is asymptotically invariant (as in the case of Poisson or Bernoulli sampling, respectively) then ([xi]n) is asymptotically exchangeable, and the associated empirical distribution converges to the corresponding product random measure.

Keywords: Empirical; distributions; Ergodic; theorems; Exchangeable; sequences; Poisson; and; Bernoulli; sampling; Random; thinning (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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