scholarly journals Large deviations for random evolutions with independent increments in the scheme of the Poisson approximation

2013 ◽  
Vol 85 ◽  
pp. 107-114 ◽  
Author(s):  
I. V. Samoĭlenko
Keyword(s):  
Large Deviations ◽  
Poisson Approximation ◽  
Independent Increments ◽  
Random Evolutions

Large deviations for random evolutions with independent increments in the scheme of Lévy approximation with split and double merging

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Igor V. Samoilenko
Keyword(s):  
Asymptotic Analysis ◽  
Large Deviations ◽  
Process With Independent Increments ◽  
Independent Increments ◽  
Exponential Generator ◽  
Random Evolutions

AbstractAsymptotic analysis of the problem of large deviations for random evolutions with independent increments in the circuit of Lévy approximation with split and double merging is carried out. Large deviations for random evolutions in the circuit of Lévy approximation with split and double merging are determined by the exponential generator for the jumping process with independent increments.

Estimating statistical significance of sequence alignments

1994 ◽  
Vol 344 (1310) ◽  
pp. 383-390 ◽  
Keyword(s):  
Molecular Biology ◽  
Large Deviations ◽  
Dna Sequences ◽  
Upper Bound ◽  
Statistical Significance ◽  
Poisson Approximation ◽  
Linear Case ◽  
Sequence Alignments ◽  
Random Sequences ◽  
Hoeffding Inequality

Algorithms that compare two proteins or DNA sequences and produce an alignment of the best matching segments are widely used in molecular biology. These algorithms produce scores that when comparing random sequences of length n grow proportional to n or to log (n) depending on the algorithm parameters. The Azuma-Hoeffding inequality gives an upper bound on the probability of large deviations of the score from its mean in the linear case. Poisson approximation can be applied in the logarithmic case.

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