Limit theorems for distributions of sums reduced modulo a

Horand Störmer

Stochastic Processes and their Applications, 1986, vol. 22, issue 2, 343-347

Abstract: Let X1, X2,... be independent random variables and define . Let partition of into intervals , of any fixed length a > 0 be given. We ask for the distribution of the remainder Sn-kna where[kna (kn+1)a) is the random interval con Sn. Necessary and sufficient conditions are given for this distribution to converge to the uniform distribution in [0, a] as n-->[infinity].

Keywords: renewal; processes; sums; of; random; variables; reduced; modulo; a; limit; theorems; convergence; to; uniform; distribution (search for similar items in EconPapers)
Date: 1986
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