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Integro-local theorems for sums of independent random vectors in the series scheme |
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| Authors: | A. A. Borovkov A. A. Mogul’skii |
| Affiliation: | (1) S. L. Sobolev Mathematics Institute, Novosibirsk, Sibirian Branch, Russian Academy of Sciences, Russia |
| 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 |
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