A quantum-mechanical functional central limit theorem

A. M. Cockroft, S. P. Gudder and R. L. Hudson

Journal of Multivariate Analysis, 1977, vol. 7, issue 1, 125-148

Abstract: Continuing an earlier work [4], properties of canonical Wiener processes are investigated. An analog of the sample path continuity property is obtained. A noncommutative counterpart of weak convergence is formulated. Operator processes (Pn, Qn) analogous to the random-walk approximating processes of the Donsker invariance principle are defined in terms of a sequence (pi, qi) of pairs of quantum mechanical canonical observables satisfying hypotheses analogous to those of the classical central limit theorem. It is shown that Pn, Qn) converges weakly to a canonical Wiener process.

Keywords: canonical; quantum-mechanics; Wiener; process; functional; central; limit; theorem (search for similar items in EconPapers)
Date: 1977
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