Weak Convergence Results for Multiple Generations of a Branching Process

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms of several generations of such processes. Applications of our main result include a functional central limit theorem (CLT), a Darling-Erd\"os result, and an extremal process result. The limiting process for our functional CLT is an infinite dimensional Brownian motion with sample paths in the infinite product space $(C_0[0,1])^{\infty}$, with the product topology, or in Banach subspaces of $(C_0[0,1])^{\infty}$ determined by norms related to the distribution of the population size of the branching process. As an application of this CLT we obtain a central limit theorem for ratios of weighted sums of generations of a branching processes, and also to various maximums of these generations. The Darling-Erd\"os result and the application to extremal distributions also include infinite dimensional limit laws. Some branching process examples where the CLT fails are also included.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Weak Convergence Results for Multiple Generations of a Branching Process 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 Convergence Results for Multiple Generations of a Branching Process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak Convergence Results for Multiple Generations of a Branching Process will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-269342

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.