The Lukacs theorem and the Olkin-Baker equation
Roman Ger , Jolanta Misiewicz , Jacek Wesołowski
AbstractThe 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.
|Journal series||arXiv:1112.1226, (0 pkt)|
|Keywords in English||26A99, 26A15, 60E05, Mathematics - Probability|
|Publication indicators||= 5|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.