English, Article, Journal or magazine article edition: Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables Peter J. Hammond; Yeneng Sun

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Bookmark: http://trove.nla.gov.au/version/142708
Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables
Author
  • Peter J. Hammond
  • Yeneng Sun
Physical Description
  • preprint
Notes
  • April 2000 As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes using a natural ``one-way Fubini'' property that guarantees a unique meaningful solution to this joint measurability problem when the random variables are independent even in a very weak sense. In particular, if F is the smallest extension of the usual product sigma-algebra such that the process is measurable, then there is a unique probability measure v on F such that the integral of any v-integrable function is equal to a double integral evaluated in one particular order. Moreover, in general this measure cannot be further extended to satisfy a two-way Fubini property. However, the extended framework with the one-way Fubini property not only shares many desirable features previously demonstrated under the stronger two-way Fubini property, but also leads to a new characterization of the most basic probabilistic concept --- stochastic independence in terms of regular conditional distributions.
  • RePEc:wop:stanec:00008
Language
  • English
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