Self-similar and Markov composition structures |
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Authors: | A Gnedin J Pitman |
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Institution: | (1) Utrecht University, The Netherlands;(2) University of California, Berkeley, USA |
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Abstract: | 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 that 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 1’s in the sequence are the positions 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 presented in previous papers,
we identify self-similar Markov composition structures associated with the two-parameter family of partition structures. Bibliography:
19 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 59–84. |
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Keywords: | |
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