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Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 3, Pages 457–467 (Mi tvp2715)  

The limit theorems for some functionals of processes with independent increments

Yu. A. Davydov

Leningrad

Abstract: This paper deals with asymptotical behaviour of the distribution of the functional $\frac1{D_T}\int_0^Th(S_t) dt$, where $S_t$ is a stochastic process with independent and stationary increments, $h(x)$ is a bounded function such that
$$ \frac1{T^\beta}\int_0^Th(x) dx\to p,\quad\frac1{T^\beta}\int_{-T}^0h(x) dx\ge q,\quad T\to\infty,\quad0\le\beta\le1 $$
and $D_T$ is a normalizing factor.

Full text: PDF file (555 kB)

English version:
Theory of Probability and its Applications, 1974, 18:3, 431–441

Bibliographic databases:

Received: 20.07.1972

Citation: Yu. A. Davydov, “The limit theorems for some functionals of processes with independent increments”, Teor. Veroyatnost. i Primenen., 18:3 (1973), 457–467; Theory Probab. Appl., 18:3 (1974), 431–441

Citation in format AMSBIB
\Bibitem{Dav73}
\by Yu.~A.~Davydov
\paper The limit theorems for some functionals of processes with independent increments
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 3
\pages 457--467
\mathnet{http://mi.mathnet.ru/tvp2715}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=324779}
\zmath{https://zbmath.org/?q=an:0301.60047}
\transl
\jour Theory Probab. Appl.
\yr 1974
\vol 18
\issue 3
\pages 431--441
\crossref{https://doi.org/10.1137/1118058}


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