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Independent sampling of a stochastic process

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  • Glynn, Peter
  • Sigman, Karl

Abstract

We investigate the question of when sampling a stochastic process X={X(t):Â t[greater-or-equal, slanted]0} at the times of an independent point process [psi] leads to the same empirical distribution as the time-average limiting distribution of X. Two main cases are considered. The first is when X is asymptotically stationary and ergodic, and [psi] satisfies a mixing condition. In this case, the pathwise limiting distributions in function space are shown to be the same. The second main case is when X is only assumed to have a constant finite time average and [psi] is assumed a positive recurrent renewal processes with a spread-out cycle length distribution. In this latter case, the averages are shown to be the same when some further conditions are placed on X and [psi].

Suggested Citation

  • Glynn, Peter & Sigman, Karl, 1998. "Independent sampling of a stochastic process," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 151-164, June.
  • Handle: RePEc:eee:spapps:v:74:y:1998:i:2:p:151-164
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    References listed on IDEAS

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    8. Lii, Keh-Shin & Masry, Elias, 1994. "Spectral estimation of continuous-time stationary processes from random sampling," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 39-64, August.
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