Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables

Details Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables

2011-11-08

arxiv.org/abs/1111.1786v2

Mathematics

Probability

Scientific paper

We show that when $\set{X_j}$ is a sequence of independent (but not necessarily identically distributed) random variables which satisfies a condition similar to the Lindeberg condition, the properly normalized geometric sum $\sum_{j=1}^{\nu_p}X_j$ (where $\nu_p$ is a geometric random variable with mean $1/p$) converges in distribution to a Laplace distribution as $p\to 0$. The same conclusion holds for the multivariate case. This theorem provides a reason for the ubiquity of the double power law in economic and financial data.

Affiliated with

Also associated with

No associations

Rating

Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables 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 Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak Limit of the Geometric Sum of Independent But Not Identically Distributed Random Variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52904