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Teor. Veroyatnost. i Primenen., 1967, Volume 12, Issue 3, Pages 551–559 (Mi tvp738)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Integral equations and some limit theorems for additive functionals of Markov processes

N. I. Portenko

Donetsk

Abstract: Integral equation (3) where $V(dy)$ is a signed measure and $p(s,x,y)$ is the transition density function of a Markov process $\xi_t$ is considered. Under some conditions the solution of this equation can be considered as the characteristic function of some functional of the process
$$ \int_0^t\frac{dV}{dx}(\xi_s) ds $$
where $\frac{dV}{dx}(x)$ is a generalized function. Using the results obtained we prove a limit theorem for additive functionals of a sequence of sums of independent random variables with distributions tending to a stable distribution of index $\alpha$, $1<\alpha\le2$.

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English version:
Theory of Probability and its Applications, 1967, 12:3, 500–505

Bibliographic databases:

Received: 04.07.1966

Citation: N. I. Portenko, “Integral equations and some limit theorems for additive functionals of Markov processes”, Teor. Veroyatnost. i Primenen., 12:3 (1967), 551–559; Theory Probab. Appl., 12:3 (1967), 500–505

Citation in format AMSBIB
\Bibitem{Por67}
\by N.~I.~Portenko
\paper Integral equations and some limit theorems for additive functionals of Markov processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1967
\vol 12
\issue 3
\pages 551--559
\mathnet{http://mi.mathnet.ru/tvp738}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=221596}
\zmath{https://zbmath.org/?q=an:0178.20202}
\transl
\jour Theory Probab. Appl.
\yr 1967
\vol 12
\issue 3
\pages 500--505
\crossref{https://doi.org/10.1137/1112061}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Borodin, “Brownian local time”, Russian Math. Surveys, 44:2 (1989), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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