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A projective central limit theorem and interacting Fock space representation for the limit process. (English) Zbl 1140.46324

Bozejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. Papers presented at the 9th workshop, Bȩdlewo, Poland, September 29–October 10, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 78, 69-80 (2008).
Summary: Accardi et al. proved a central limit theorem, based on the notion of projective independence. In this note, we use the symmetric projective independence to present a new version of that result, where the limiting process is perturbed by the insertion of suitable test functions. Moreover, we give a representation of the limit process in 1-mode type interacting Fock space.
For the entire collection see [Zbl 1128.46002].

MSC:

46L53 Noncommutative probability and statistics
60B99 Probability theory on algebraic and topological structures
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