The central limit theorem for Carleman's equation

H. P. McKean

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this paper is to discuss the analogy between the law of large numbers and the central limit theorem of classical probability theory on the one hand and the hydrodynamical approximations in the statistical mechanics of gases on the other. The chief illustration is provided by Carleman's model [2] for which the central limit approximation is a kind of non-linear Brownian motion regulated by ∂n/∂t=(n'/n).

Original languageEnglish (US)
Pages (from-to)54-92
Number of pages39
JournalIsrael Journal of Mathematics
Volume21
Issue number1
DOIs
StatePublished - Mar 1975

ASJC Scopus subject areas

  • Mathematics(all)

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