Independent sampling of a stochastic process

Peter Glynn and Karl Sigman

Stochastic Processes and their Applications, 1998, vol. 74, issue 2, 151-164

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].

Keywords: Time; average; Event; average; Independent; sampling; Asymptotically; stationary; ergodic (search for similar items in EconPapers)
Date: 1998
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