Abstract: We consider three new schemes of random splitting of a unit interval. These schemes are related to settings considered earlier in literature. Essentially we are concerned with asymptotic behavior of sequences of subdivisions. In all three cases almost sure or weak limits are obtained for a sequence of points of divisions. The two of the schemes considered are dual to each other in the sense of the contraction principle of Chamayou and Letac [2].

1991 AMS Mathematics Subject Classification: 60H25, 60J25, 60D05, 60F05, 60F15.

Key words and phrases: Splitting schemes, asymptotic behavior, Markov chains, stationary distribution, contraction principle, almost sure limits, weak limits.