Geodesic
On a Problem in Probability Theory
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 879-892.

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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. 
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V. P. Maslov; V. E. Nazaikinskii. On a Problem in Probability Theory. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 879-892. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a6/

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[2] V. P. Maslov, Negative Dimension in General and Asymptotic Topology, arXiv: math/0612543

[3] V. P. Maslov, M. V. Fedoryuk, “Logarifmicheskaya asimptotika bystroubyvayuschikh reshenii giperbolicheskikh po Petrovskomu uravnenii”, Matem. zametki, 45:5 (1989), 50–62 | MR | Zbl

[4] V. P. Maslov, Kvantovaya ekonomika, Nauka, M., 2007 | Zbl