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 Mat. Zametki, 2005, Volume 78, Issue 3, Pages 377–395 (Mi mz2595)

Nonlinear Averages in Economics

V. P. Maslov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: Kolmogorov nonlinear averaging is complemented by a natural axiom. For this averaging, we prove a theorem on large deviations as well as establish the relationship to the tunnel canonical operator.

DOI: https://doi.org/10.4213/mzm2595

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English version:
Mathematical Notes, 2005, 78:3, 347–363

Bibliographic databases:

UDC: 519

Citation: V. P. Maslov, “Nonlinear Averages in Economics”, Mat. Zametki, 78:3 (2005), 377–395; Math. Notes, 78:3 (2005), 347–363

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, “On a General Theorem of Set Theory Leading to the Gibbs, Bose–Einstein, and Pareto Distributions as well as to the Zipf–Mandelbrot Law for the Stock Market”, Math. Notes, 78:6 (2005), 807–813
2. V. P. Maslov, “Refinement of the Gibbs and Bose–Einstein Distributions”, Theoret. and Math. Phys., 145:3 (2005), 1749–1752
3. Maslov V. P., “Nonlinear averaging of entropy in number theory and a generalized law of large numbers”, Dokl. Math., 72:3 (2005), 925-929
4. Maslov V. P., “Refinement of Zipf's law for frequency dictionaries”, Dokl. Math., 72:3 (2005), 942-945
5. Maslov V. P., “The Zipf-Mandelbrot law: Quantization and an application to the stock market”, Russ. J. Math. Phys., 12:4 (2005), 483–488
6. Maslov V. P., “The large deviations law in number theory, computable functions of several arguments, and decoding”, Dokl. Math., 72:2 (2005), 766–770
7. Maslov V. P., “On the principle of increasing complexity in portfolio formation on the stock exchange”, Dokl. Math., 72:2 (2005), 718–722
8. V. P. Maslov, “The Lack-of-Preference Law and the Corresponding Distributions in Frequency Probability Theory”, Math. Notes, 80:2 (2006), 214–223
9. V. P. Maslov, “On a new rank distribution”, Math. Notes, 80:3 (2006), 447–448
10. V. P. Maslov, “Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law”, Math. Notes, 80:6 (2006), 806–813
11. Maslov V. P., “Quantum linguistic statistics”, Russ. J. Math. Phys., 13:3 (2006), 315–325
12. V. P. Maslov, “Zeroth-order phase transitions and Zipf law quantization”, Theoret. and Math. Phys., 150:1 (2007), 102–122
13. V. P. Maslov, “General Notion of a Topological Space of Negative Dimension and Quantization of Its Density”, Math. Notes, 81:1 (2007), 140–144
14. V. P. Maslov, “Densities of Lattices Corresponding to Spaces of Positive, Negative, and Variational Dimension, and Their Application to Time Series”, Math. Notes, 81:1 (2007), 222–233
15. Maslov V. P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95
16. V. P. Maslov, “Quasithermodynamics and a Correction to the Stefan–Boltzmann Law”, Math. Notes, 83:1 (2008), 72–79
17. V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813
18. Maslov V. P., “New Look at Thermodynamics of Gas and at Clusterization”, Russ. J. Math. Phys., 15:4 (2008), 493–510
19. Maslov V. P., “On the superfluidity of classical liquid in nanotubes. IV”, Russ. J. Math. Phys., 15:2 (2008), 280–290
20. Maslov V. P., “On the new distribution generalizing the Gibbs, Bose–Einstein, and Pareto distributions”, Math. Notes, 85:5-6 (2009), 613–622
21. Dyakonov K. M., “Kolmogorov averages and approximate identities”, Constr. Approx., 30:1 (2009), 17–31
22. Maslov V. P., “Thermodynamics of fluids for imperfect gases with Lennard-Jones interaction potential. I”, Math. Notes, 86:3–4 (2009), 522–529
23. Maslov V. P., “Phase transitions of the first and second kind as economic crises. Abstract thermodynamics of fluids”, Russ. J. Math. Phys., 16:3 (2009), 323–344
24. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 239–279
25. M. A. Guzev, E. Yu. Nikitina, “Rangovyi analiz Ugolovnogo Kodeksa RF (na primere ekonomicheskikh prestuplenii)”, Dalnevost. matem. zhurn., 10:2 (2010), 117–129
26. M. A. Guzev, A. A. Dmitriev, “On the Critical Points of the Kolmogorov Mean with Constraints on the Mean of the Arguments”, Math. Notes, 98:2 (2015), 237–250
27. Zegarlinski B., “Linear and Nonlinear Dissipative Dynamics”, Rep. Math. Phys., 77:3 (2016), 377–397
28. M. A. Guzev, G. Sh. Tsitsiashvili, M. A. Osipova, “Zaschita setevoi struktury avtonomnymi apparatami”, Dalnevost. matem. zhurn., 18:2 (2018), 177–182
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