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Abstract  

A mathematical treatment is given for the family of scientometric laws (usually referred to as the Zipf-Pareto law) that have been described byPrice and do not conform with the usual Gaussian view of empirical distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions. An analysis of the Zipf-Pareto law in relationship with stable non Gaussian distributions reveals, in particular, that the truncated Cauchy distribution asymptotically coincides with Lotka's law, the most well-known frequency form of the Zipf-Pareto law. The mathematical theory of stable non Gaussian distributions, as applied to the analysis of the Zipf-Pareto law, leads to several conclusions on the mechanism of their genesis, the specific methods of processing empirical data, etc. The use of non-Gaussian processes in scientometric models suggests that this approach may result in a general mathematical theory describing the distribution of science related variables.

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Gaussian Processes with Stationary Increments under Holder norms , J. Theoret. Probab. 8 ( 1995 ), 361 – 386 . MR 96b:60096 [8] L i , W. V. and L inde , W

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Adler, R. J. , An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes , Institute of Mathematical Statistics Lecture Notes — Monograph Series 12

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Abstract  

Generalized random processes are classified by various types of continuity. Representation theorems of a generalized random process on

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{Mp} on a set with arbitrary large probability, as well as representations of a correlation operator of a generalized random process on
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{Mp} and Lr(R), r > 1, are given. Especially, Gaussian generalized random processes are proven to be representable as a sum of derivatives of classical Gaussian processes with appropriate growth rate at infinity. Examples show the essence of all the proposed assumptions. In order to emphasize the differences in the concept of generalized random processes defined by various conditions of continuity, the stochastic differential equation y′(ω; t) = f(ω; t) is considered, where y is a generalized random process having a point value at t = 0 in the sense of Lojasiewicz.

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. 6 547 577 KUELBS, J., LI, W. V. and SHAO, Q.-M., Small ball probabilities for Gaussian processes with stationary increments under Hölder norms, J

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Watanabe, H. , Asymptotic properties of Gaussian processes, Ann. Math. Statist. , 43 (1972), 580–596. MR 46 #6438 Watanabe H. Asymptotic properties of Gaussian processes

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23 467 469 WASAN, M. T., On an inverse Gaussian process, Skand. Aktuarietidskr. 1968 (1968), 69-96. MR 39 #3574 On an

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Gaussian processes, Ann. Math. Statist. , 43 (1972), 580–596. MR 46 #6438 Watanabe H. Asymptotic properties of Gaussian processes Ann. Math. Statist

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209 – 224 10.1023/A:1021655227120 . [8] Kolmogorov , A. N. , Rozanov , H. 1960 On strong mixing for stationary Gaussian processes Theory Probab. Appl. 5 204 – 208 10

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stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling , Computers and Geotechnics , Vol. 63 , 2015 , pp. 13 – 25 . [11] Guillaume

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