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Donsker's Delta Function and the Covariance between Generalized Functionals
Author(s) -
Benth Fred Espen,
Ng Siu-Ah
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003319
Subject(s) - covariance , white noise , mathematics , dirac delta function , space (punctuation) , function (biology) , generalized function , delta , covariance function , correlation function (quantum field theory) , statistical physics , mathematical analysis , physics , statistics , computer science , spectral density , astronomy , biology , operating system , evolutionary biology
A classical space and a nonstandard space are used as models for white noise. The expectation of the product of certain generalized functionals is first proved to be finite. Then the covariance and the correlation between Donsker's delta functions are calculated and given meaning.