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Zapiski Nauchnykh Seminarov LOMI, 1977, Volume 72, Pages 92–97 (Mi znsl1964)  

A class of limit distributions for maximum cumulative sum

V. B. Nevzorov
Abstract: Let $X_1,X_2,\dots$ be a sequence of independent identically distributed random variables with zero mathematical expectation and finite variances. $S_0=0$ and $S_n\sum^n_{i=1}X_i$. It is proved that $G_a(x)= \begin{cases} 0, & \text{\rm{ if }}x\leqslant a,\\ \dfrac{\Phi(x)-\Phi(a)}{1-\Phi(a)}, & \text{\rm{ if }}x\geqslant a. \end{cases}$ is the limit distribution function of the normalized random variable $\overline S_n=\max_{0\leqslant k\leqslant n}\{S_k+a(k,n)\}$ for some sequence of centering constants $a(k,n)$.
English version:
Journal of Soviet Mathematics, 1983, Volume 23, Issue 3, Pages 2286–2290
DOI: https://doi.org/10.1007/BF01682804
Bibliographic databases:
UDC: 519.65
Language: Russian
Citation: V. B. Nevzorov, “A class of limit distributions for maximum cumulative sum”, Problems of the theory of probability distributions. Part IV, Zap. Nauchn. Sem. LOMI, 72, "Nauka", Leningrad. Otdel., Leningrad, 1977, 92–97; J. Soviet Math., 23:3 (1983), 2286–2290
Citation in format AMSBIB
\Bibitem{Nev77}
\by V.~B.~Nevzorov
\paper A class of limit distributions for maximum cumulative sum
\inbook Problems of the theory of probability distributions. Part~IV
\serial Zap. Nauchn. Sem. LOMI
\yr 1977
\vol 72
\pages 92--97
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1964}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=474471}
\zmath{https://zbmath.org/?q=an:0517.60020|0405.60033}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 23
\issue 3
\pages 2286--2290
\crossref{https://doi.org/10.1007/BF01682804}
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