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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 3, Pages 551–559
(Mi tvp738)
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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 $\alpha$, $1<\alpha\le2$.
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
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https://www.mathnet.ru/eng/tvp738 https://www.mathnet.ru/eng/tvp/v12/i3/p551
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Abstract page: | 261 | Full-text PDF : | 122 |
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