Integro-local theorems for sums of independent random vectors in the series scheme

Authors: Borovkov, A.¹; Mogul'skii, A.²

Source: Mathematical Notes, Volume 79, Number 3, March 2006 , pp. 468-482(15)

Publisher: Springer

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Abstract:

Let S(n) = ξ(1)+…+ξ(n) be a sum of independent random vectors ξ(i) = ξ _(n)(i) with general distribution depending on a parameter n. We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability P(S(n) ∈ Δ[x), where Δ[x) is a cube with edge Δ and vertex at a point x.

Keywords: independent identically distributed random vectors; summation theory; integro-local theorems; limit theorems; large deviations; weak convergence

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11006-006-0053-3

Affiliations: 1: Email: borovkov@math.nsc.ru 2: Email: mogul@math.nsc.ru

Publication date: 2006-03-01