Self-similar and Markov composition structures

الأصل · EN

The bijection between composition structures and random closed subsets of the unit interval implies that the composition structures associated with S ∩ [0,1] for a self-similar random set S⊂ R+ are those which are consistent with respect to a simple truncation operation. Using the standard coding of compositions by finite strings of binary digits starting with a 1, the random composition of n is defined by the first n terms of a random binary sequence of infinite length. The locations of 1s in the sequence are the places visited by an increasing time-homogeneous Markov chain on the positive integers if and only if S = (-W) for some stationary regenerative random subset W of the real line. Complementing our study in previous papers, we identify self-similar Markovian composition structures associated with the two-parameter family of partition structures.