The Lukacs theorem and the Olkin-Baker equation

Roman Ger , Jolanta Misiewicz , Jacek Wesołowski

Abstract

The Olkin-Baker functional equation is closely related to the celebrated Lukacs characterization of the gamma distribution. Its deeper understanding is essential to settle a challenging question of multivariate extensions of the Lukacs theorem. In this paper, first, we provide a new approach to the additive Olkin-Baker equation which holds almost everywhere on (0,\\textbackslash\infinity)\\textasciicircum\2 (with respect to the Lebesgue measure on R\\textasciicircum\2) under measurability assumption. Second, this new approach is adapted to the case when unknown functions are allowed to be non-measurable and the complete solution is given in such a general case. Third, the Olkin-Baker equation holding outside of a set from proper linearly invariant ideal of subsets of R\\textasciicircum\2 is considered.
Author Roman Ger
Roman Ger,,
-
, Jolanta Misiewicz (FMIS / DPMS)
Jolanta Misiewicz,,
- Department of Probability and Mathematical Statistics
, Jacek Wesołowski (FMIS / DPMS)
Jacek Wesołowski,,
- Department of Probability and Mathematical Statistics
Journal seriesarXiv:1112.1226, (0 pkt)
Issue year2011
Keywords in English26A99, 26A15, 60E05, Mathematics - Probability
URL http://arxiv.org/abs/1112.1226
Score (nominal)0
Publication indicators WoS Citations = 5
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?