Extracting information from random data. Applications of laws of large numbers in technical sciences and statistics
Pawe{\l} J. Szab{\l}owski
TL;DR
This paper explores the theoretical foundations of the Laws of Large Numbers, linking them to various areas of mathematical analysis, and demonstrates their applications in statistical estimation and stochastic processes.
Contribution
It formulates conditions for convergence of Laws of Large Numbers and connects them with summation theory and orthogonal series, highlighting their practical applications.
Findings
Established conditions for convergence of Laws of Large Numbers
Linked Laws of Large Numbers with summation theory and orthogonal series
Demonstrated applications in stochastic approximation and statistical estimation
Abstract
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large Numbers such as Stochastic Approximation, Density and Regression Estimation, Identification.
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Taxonomy
TopicsNeural Networks and Applications · Numerical Methods and Algorithms · Probability and Risk Models