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A geometry on the space of probabilities (II). Projective spaces and exponential families.

Henryk Gzyl, Lázaro Recht (2006)

Revista Matemática Iberoamericana

In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities (I). The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a...

A projective central limit theorem and interacting Fock space representation for the limit process

Vitonofrio Crismale (2007)

Banach Center Publications

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.

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