Asymptotic Behavior of Continuous Set-Indexed Martingales

Diane Saada ()
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Diane Saada: Bar Ilan University

Journal of Theoretical Probability, 2001, vol. 14, issue 2, 319-332

Abstract: Abstract In this paper, following the Knight's approach, we solve a convergence problem for set-indexed martingales. For this purpose, we first define a tightness criterion for set-indexed continuous processes. The core of this characterization is connected with a weaker definition of continuity and hence the use of the corresponding topology, and with the fact that indices take values in a semilattice of closed subsets. Then, we give an effective tightness criterion by means of an estimate for a majorizing measure defined on the space. We finally prove under this set-indexed framework a theorem similar to the Knight's.

Keywords: set-indexed martingales; continuous processes; tightness criterion (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011103428410

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