Perfect i.i.d Processes
Asian Journal of Probability and Statistics · pp. 41–45 · Published 11 Jul 2022
10.9734/ajpas/2022/v18i230443Abstract
This note proves a theorem about i.i.d. i.e. independent and indentically distributed processes, when the index space is a measure space. The statement of the problem corresponding to the theorem proved in this paper appears in [1], in which the concept of a sample distribution limit corresponds to the concept of a perfect i.i.d process in this paper. Theorems proved in this theme, regarding existing and non-existence, have been shown in the economics literature, when the index set is [0; 1], in [2], [3], [4], [5]. The approach taken in this paper is perhaps, surprisingly elementary. We may apply standard measure extension theorems to show existence. These may be found in [6], [7].
References (7)
- 1 Infinite Dimensional Analysis: A Hitchhiker's Guide [DOI]
- 2 The law of large numbers with a continuum of IID random variables [DOI]
- 3 An Introduction to Measure Theory [DOI]
- 4 An expository note on individual risk without aggregate uncertainty [DOI]
- 5 A law of large numbers for large economies [DOI]
- 6 RANDOM MEASURE PRESERVING TRANSFORMATIONS [DOI]
- 7 Measure Theory and Fine Properties of Functions [DOI]
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