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Mat. Zametki, 2007, Volume 81, Issue 6, Pages 879–892 (Mi mz3738)  

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 $x=(x_1,…,x_s)$, uniformly distributed on the set
$$ x_j\ge0,\quad j=1,…,s;\qquad \sum_{j=1}^sx_j=N,\quad \sum_{j=1}^s\lambda_jx_j\le E. $$
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

DOI: https://doi.org/10.4213/mzm3738

Full text: PDF file (550 kB)
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English version:
Mathematical Notes, 2007, 81:6, 788–799

Bibliographic databases:

UDC: 519
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. P. Maslov, “Nonstandard analysis, parastatistics, and fractals”, Theoret. and Math. Phys., 153:2 (2007), 1575–1581  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. P. Maslov, “Quasithermodynamics and a Correction to the Stefan–Boltzmann Law”, Math. Notes, 83:1 (2008), 72–79  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. P. Maslov, “New distribution formulas for classical gas, clusters, and phase transitions”, Theoret. and Math. Phys., 157:2 (2008), 1577–1594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математические заметки Mathematical Notes
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