Asymptotically invariant sampling and averaging from stationary-like processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:82

Article

Kallenberg, O

关键词: empirical distributions;    ergodic theorems;    exchangeable sequences;    Poisson and Bernoulli sampling;    random thinning;   

DOI  :  10.1016/S0304-4149(99)00009-5

来源: Elsevier

【 摘 要 】

Given a process X on R-d or Z(d), 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. (C) 1999 Elsevier Science B.V. All rights reserved. MSC. primary 60G09-10; secondary 28D99.

【 授权许可】

Free