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A conditional limit theorem with a random number of summands
S. G. Gushchin
Abstract:
For a sequence of independent identically distributed random vectors
with integer-valued non-negative components
$(\xi_1^{(i)},\ldots,\xi_s^{(i)},\eta_i)$, $i=1,2,\dots$,
we prove a limit theorem for the joint distribution of the sums
$$
\sum_{i=1}^m \xi_j^{(i)}, \qquad j=1,\dots,s,
$$
for $n\to\infty$ and the random $m$ determined by the condition
$$
\sum_{i=1}^m \eta_i = n.
$$
Received: 20.02.1995
Citation:
S. G. Gushchin, “A conditional limit theorem with a random number of summands”, Diskr. Mat., 9:2 (1997), 131–138; Discrete Math. Appl., 7:3 (1997), 305–312
Linking options:
https://www.mathnet.ru/eng/dm466https://doi.org/10.4213/dm466 https://www.mathnet.ru/eng/dm/v9/i2/p131
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Abstract page: | 293 | Full-text PDF : | 162 | First page: | 1 |
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