Statistical Convergence in Probability for a Sequence of Random Functions

Celaleddin Şençimen ()
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Celaleddin Şençimen: Mehmet Akif Ersoy University

Journal of Theoretical Probability, 2013, vol. 26, issue 1, 94-106

Abstract: Abstract In this paper, we introduce a new type of convergence for a sequence of random functions, namely, statistical convergence in probability, which is a natural generalization of convergence in probability. In this approach, we allow such a sequence to go far away from the limit point infinitely many times by presenting random deviations, provided that these deviations are negligible in some sense of measure. In this context, the set of values of a random function is considered as a probabilistic metric (PM) space of random variables, and some basic results are obtained using the tools of PM spaces.

Keywords: Random function; E-space; Statistical convergence in probability; 60G05; 40A35; 54E70 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0346-7

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