Implicit Renewal Theory and Power Tails on Trees

Details Implicit Renewal Theory and Power Tails on Trees Implicit Renewal Theory and Power Tails on Trees

2010-06-16

arxiv.org/abs/1006.3295v4

Mathematics

Probability

Scientific paper

We extend Goldie's (1991) Implicit Renewal Theorem to enable the analysis of recursions on weighted branching trees. We illustrate the developed method by deriving the power tail asymptotics of the distributions of the solutions R to: R =_D sum_{i=1}^N C_i R_i + Q, R =_D max(max_{i=1}^N C_i R_i, Q), and similar recursions, where (Q, N, C_1,..., C_N) is a nonnegative random vector with N in {0, 1, 2, 3, ..., infinity}, and {R_i}_{i >= 1} are iid copies of R, independent of (Q, N, C_1,..., C_N); =_D denotes the equality in distribution.

Affiliated with

Also associated with

No associations

Rating

Implicit Renewal Theory and Power Tails on Trees 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 Implicit Renewal Theory and Power Tails on Trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Implicit Renewal Theory and Power Tails on Trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101198