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This article is cited in 3 scientific papers (total in 3 papers)
On a Problem in Probability Theory
V. P. Maslova, V. E. Nazaikinskiib a M. V. Lomonosov Moscow State University, Faculty of Physics
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
Abstract:
For continuous random variables, we study a problem similar to that considered earlier by one of the authors for discrete random variables. Let numbers
$$
N>0,\qquad
E>0,\qquad
0\le\lambda_1\le\lambda_2\le\dotsb\le\lambda_s
$$
be given. Consider a random vector $x=(x_1,\dots,x_s)$, uniformly distributed on the set
$$
x_j\ge0,\quad
j=1,\dots,s;\qquad
\sum_{j=1}^sx_j=N,\quad
\sum_{j=1}^s\lambda_jx_j\le E.
$$
We study the weak limit of $x$ as $s\to\infty$.
Keywords:
dependent random variable, uniform distribution, weak limit, Heaviside function, risk-free investment, budget and priority constraints.
Received: 10.04.2007
Citation:
V. P. Maslov, V. E. Nazaikinskii, “On a Problem in Probability Theory”, Mat. Zametki, 81:6 (2007), 879–892; Math. Notes, 81:6 (2007), 788–799
Linking options:
https://www.mathnet.ru/eng/mzm3738https://doi.org/10.4213/mzm3738 https://www.mathnet.ru/eng/mzm/v81/i6/p879
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