The Method of Optimal Nonlinear Extrapolation of Vector Random Sequences on the Basis of Polynomial Degree Canonical Expansion

2018 ◽  
pp. 14-25 ◽  
Author(s):  
Vyacheslav S. Shebanin ◽  
Yuriy P. Kondratenko ◽  
Igor P. Atamanyuk
Keyword(s):  
Random Sequences ◽  
Polynomial Degree ◽  
Canonical Expansion

Asymptotic behavior of the records of multivariate random sequences in a norm sense

2020 ◽  
Vol 70 (6) ◽  
pp. 1457-1468
Author(s):  
Haroon M. Barakat ◽  
M. H. Harpy
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Sufficient Conditions ◽  
Record Values ◽  
Necessary And Sufficient Conditions ◽  
Random Sequences ◽  
Necessary And Sufficient

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

On the structure of polynomial roots

2021 ◽  
Vol 105 (563) ◽  
pp. 253-262
Author(s):  
R. W. D. Nickalls
Keyword(s):  
Underlying Structure ◽  
Polynomial Roots ◽  
Polynomial Degree

This Article explores how root multiplicity and polynomial degree influence the structure of the roots of a univariant polynomial. After setting up the notation, we draw upon a result derived in [1], and show that all polynomial roots have a common underlying structure comprising just five parameters. Finally we present some examples involving the lower polynomials.

Sampling multidimensional signals by a new class of quasi-random sequences

2010 ◽  
Vol 23 (1-2) ◽  
pp. 237-253 ◽  
Author(s):  
Ewa Skublska-Rafajłowicz ◽  
Ewaryst Rafajłowicz
Keyword(s):  
Random Sequences ◽  
New Class ◽  
Multidimensional Signals

Asymptotic properties of a certain class of Bush–Mosteller learning models

1980 ◽  
Vol 12 (4) ◽  
pp. 922-941
Author(s):  
Peter Findeisen
Keyword(s):  
Necessary Conditions ◽  
Asymptotic Properties ◽  
Response Sequence ◽  
Positive Probability ◽  
Learning Models ◽  
Random Sequences ◽  
Learning Experiment ◽  
Sufficient And Necessary Conditions

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.

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