In a recent paper  , Nicolas Bouleau provides a new tool, based on the language of Dirichlet forms, to study the propagation of errors and reinforce the historical approach of Gauss. In the same way that the practical use of the normal distribution in statistics may be explained by the central limit theorem, the aim of this paper is to underline the importance of a family of error structures by asymptotic arguments. Source Osaka J. Zentralblatt MATH identifier
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Toggle navigation. Have you forgotten your login? Other publications. Hide details. Abstract : In this paper we consider some elementary and fair zero-sum games of chance to study the impact of random effects on the wealth distribution of N interacting players.
Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties, in particular, we underscore that randomness plays a key role in concentrating the wealth to the extreme with a single player.
From a mathematical perspective, we interestingly recover for small and high-frequency transactions some diffusion limits extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms. We show that taxation of income is not sufficient to overcome the externe concentration process contrary to a uniform taxation of capital that stabilizes the economy preventing agents to be ruined.
Identifiers HAL Id : halshs, version 2. Citation Nicolas Bouleau, Christophe Chorro. The impact of randomness on the distribution of wealth: Some economic aspects of the Wright-Fisher diffusion process.
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