Lower Bounds for Probabilities of Embedding with Arbitrary Margin

Authors: Mezhennaya N.M. , Mikhailov V.G.  Published: 08.09.2013
Published in issue: #2(45)/2012  

Category: Mathematics  
Keywords: embedding with a margin, sequence over the finite alphabet, lower bounds

The notion of compact embedding introduced by J. Golic is generalized. The lower estimations are deduced for the mathematical expectation of the probability of embedding with a given margin a segment of the sequence of independent equally distributed random quantities over the N-element alphabet into the sequence of independent random quantitieshaving the uniform distribution on the same alphabet. These estimations refine the known evaluations for the probability of embedding with a given margin and, in particular, for the probability of compact embedding.