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.
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Translated from Matematicheskie Zametki, vol. 79, no. 4, 2006, pp. 505–521.
Original Russian Text Copyright ©2006 by A. A. Borovkov, A. A. Mogul’skii.
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Borovkov, A.A., Mogul’skii, A.A. Integro-local theorems for sums of independent random vectors in the series scheme. Math Notes 79, 468–482 (2006). https://doi.org/10.1007/s11006-006-0053-3
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DOI: https://doi.org/10.1007/s11006-006-0053-3