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Stochastic processes with independent increments for random mappings

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Abstract

Using additive functions defined on the combinatorial structure of all mappings of anN set into itself, we define paths in the space\(\mathbb{D}[0,1]\) endowed with the Skorokhod topology. Taking a mapping with equal probability, we get a sequence of random processes. Necessary and sufficient conditions for the weak convergence of this sequence to a stochastic process with independent increments are established. It is shown that the class of such processes contains all possible limits, provided that, on the components of a mapping, the additive functions have values small in average.

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Authors
  1. E. Manstavičius
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Additional information

Partially supported by the Lithuanian State Science and Studies Foundation.

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 498–516, October–December, 1999.

Translated by E. Manstavičius

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Manstavičius, E. Stochastic processes with independent increments for random mappings. Lith Math J 39, 393–407 (1999). https://doi.org/10.1007/BF02465590

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  • DOI: https://doi.org/10.1007/BF02465590

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