Limiting processes with dependent increments for measures on symmetric group of permutations
نویسندگان
چکیده
A family of measures on the set of permutations of the first n integers, known as Ewens sampling formula, arises in population genetics. In a series of papers, the first two authors have developed necessary and sufficient conditions for the weak convergence of a partial sum process based on these measures to a process with independent increments. Under very general conditions, it has been shown that a partial sum process converges weakly in a function space if and only if a related process defined through sums of independent random variables converges. In this paper, a functional limit theory is developed where the limiting processes need not be processes with independent increments. Thus, under Ewens sampling formula, the limiting process of the partial sums of dependent variables differs from that of the associated process defined through the partial sums of independent random variables. §
منابع مشابه
Probabilistic number theory and random permutations: Functional limit theory
The ideas from Probabilistic Number Theory are useful in the study of measures on partitions of integers. Connection between the Ewens sampling formula in population genetics and the partitions of an integer generated by random permutations will be discussed. Functional limit theory for partial sum processes induced by Ewens sampling formula is reviewed. The results on limit processes with depe...
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