A refined version of the integro-local Stone theorem Full article
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Statistics and Probability Letters
ISSN: 0167-7152 |
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| Output data | Year: 2017, Volume: 123, Pages: 153-159 Pages count : 7 DOI: 10.1016/j.spl.2016.12.004 | ||||
| Tags | Asymptotic expansion; Central limit theorem; Independent identically distributed random variables; Integro-local Stone theorem; Random walk | ||||
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Abstract:
Let X,X1,X2,… be a sequence of non-lattice i.i.d. random variables with EX=0,EX=1, and let Sn:=X1+⋯+Xn, n≥1. We refine Stone's integro-local theorem by deriving the first term in the asymptotic expansion, as n→∞, for the probability P(Sn∈[x,x+Δ)), x∈R,Δ>0, and establishing uniform in x and Δ bounds for the remainder term, under the assumption that the distribution of X satisfies Cramér's strong non-lattice condition and E|X|r<∞ for some r≥3. © 2016 Elsevier B.V.
Cite:
Borovkov A.A.
, Borovkov K.A.
A refined version of the integro-local Stone theorem
Statistics and Probability Letters. 2017. V.123. P.153-159. DOI: 10.1016/j.spl.2016.12.004 WOS Scopus OpenAlex
A refined version of the integro-local Stone theorem
Statistics and Probability Letters. 2017. V.123. P.153-159. DOI: 10.1016/j.spl.2016.12.004 WOS Scopus OpenAlex
Dates:
| Published print: | Apr 1, 2017 |
Identifiers:
| Web of science: | WOS:000393266200021 |
| Scopus: | 2-s2.0-85007589314 |
| OpenAlex: | W2485183274 |