Star-scale invariant random measures

Details Star-scale invariant random measures Star-scale invariant random measures

2012-01-25

arxiv.org/abs/1201.5219v1

Mathematics

Probability

Scientific paper

In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous equation enjoys some specific properties that do not appear in the discrete star equation. To that purpose, we define a L\'evy multiplicative chaos that generalizes the already existing constructions.

Affiliated with

Also associated with

No associations

Rating

Star-scale invariant random measures 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 Star-scale invariant random measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Star-scale invariant random measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-683201