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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

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

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 $\alpha$, $1<\alpha\le2$.

Full text: PDF file (542 kB)

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

Bibliographic databases:

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} 

• http://mi.mathnet.ru/eng/tvp738
• http://mi.mathnet.ru/eng/tvp/v12/i3/p551

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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