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On the Almost Sure Convergence of Floating-Point Mantissas and Benford's Law

โœ Scribed by Peter Schatte

Publisher
John Wiley and Sons
Year
1988
Tongue
English
Weight
238 KB
Volume
135
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Let Y1, Y2, ... be a sequence of random variables 8nd let J i n be the floating-point mantissa of Y,,. Further let l f ~, ~) ( , ) denote the indicator function of the interval [I, x). If Yn/n-Z as.. wheteZ+O is 5 fnrther random variable, then the seqirence i~~,z#3fn) converges a s . to log x in the sense of -X--means and logarithmic means, respectively. The speed of convergence in this relations is estimated. -4s a conclnsion. a further argument for BEXFORD'S law is provided.

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โœ Miloje S. Radenkovic ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 151 KB ๐Ÿ‘ 2 views

In this paper, we consider the rate of convergence of the parameter estimation error and the cost function for the stochastic gradient-type algorithm. The problem is solved in the case of the minimum-variance stochastic adaptive control. It is proven that the cost function has the rate of convergenc