The Lukacs theorem and the Olkin-Baker equation

Details The Lukacs theorem and the Olkin-Baker equation The Lukacs theorem and the Olkin-Baker equation

2011-12-06

arxiv.org/abs/1112.1226v1

Mathematics

Probability

Scientific paper

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,\infinity)^2 (with respect to the Lebesgue measure on R^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^2 is considered.

Affiliated with

Also associated with

No associations

Rating

The Lukacs theorem and the Olkin-Baker equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Lukacs theorem and the Olkin-Baker equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Lukacs theorem and the Olkin-Baker equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380896