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A quantum-mechanical functional central limit theorem

Author

Listed:
  • Cockroft, A. M.
  • Gudder, S. P.
  • Hudson, R. L.

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.

Suggested Citation

  • Cockroft, A. M. & Gudder, S. P. & Hudson, R. L., 1977. "A quantum-mechanical functional central limit theorem," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 125-148, March.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:1:p:125-148
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