Geodesic
On the asymptotic normality of the
Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 144-151 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The theorem on a normal limit ($n\to\infty$) distribution of the number of false solutions of a system of nonlinear Boolean equations with independent random coefficients is proved. In particular, we assume that each equation has coefficients that take value 1 with probability that varies in some neighborhood of the point $\frac{1}{2};$ the system has a solution with the number of ones equals $\rho(n), \rho(n)\to\infty$ as $n\to\infty.$ The proof is constructed on the check of auxiliary statement conditions which in turn generalizes one well-known result.
Keywords: The nonlinear random Boolean equations, normal limit distribution, number of false solutions. 
@article{THSP_2007_13_1_a14,
     author = {Volodymyr Masol and Svitlana Slobodyan},
     title = {On the asymptotic normality of the},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {144--151},
     year = {2007},
     volume = {13},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a14/}
}
TY  - JOUR
AU  - Volodymyr Masol
AU  - Svitlana Slobodyan
TI  - On the asymptotic normality of the
JO  - Teoriâ slučajnyh processov
PY  - 2007
SP  - 144
EP  - 151
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a14/
LA  - en
ID  - THSP_2007_13_1_a14
ER  - 
%0 Journal Article
%A Volodymyr Masol
%A Svitlana Slobodyan
%T On the asymptotic normality of the
%J Teoriâ slučajnyh processov
%D 2007
%P 144-151
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a14/
%G en
%F THSP_2007_13_1_a14
Volodymyr Masol; Svitlana Slobodyan. On the asymptotic normality of the. Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 144-151. http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a14/

[1] A. M. Zubkov, B. A. Sevastianov, V. P. Chistyakov, The collection of problems in probability theory, Nauka, Moscow, 1989 (in Russian)

[2] A. M. Zubkov, “Inequalities for transitions with prohibitions”, The mathematical collection, 109 (151):4 (11) (1979), 491–532 (in Russian)

[3] V. I. Masol, “Moments of the number of solutions of system of random Boolean equations”, Random Oper. and Stoch. Equations,, 1:2 (1993), 171–179

[4] V. I. Masol, S. Y. Slobodyan, “On the convergence to the normal limit distribution of the number of false solutions of a system of nonlinear random Boolean equations”, PT, 2007 (to appear) (in Ukrainian)

[5] V. P. Chistyakov, Course of probability theory, Nauka, Moscow, 2003 (in Russian)