ar X iv : m at h / 05 05 68 7 v 1 [ m at h . PR ] 3 1 M ay 2 00 5 Self - similar and Markov composition structures ∗
نویسندگان
چکیده
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 = exp(−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.
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تاریخ انتشار 2005