Implicit Renewal Theory and Power Tails on Trees
Probability
2012-06-04 v5 Discrete Mathematics
Performance
Abstract
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.
Cite
@article{arxiv.1006.3295,
title = {Implicit Renewal Theory and Power Tails on Trees},
author = {Predrag R. Jelenković and Mariana Olvera-Cravioto},
journal= {arXiv preprint arXiv:1006.3295},
year = {2012}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1012.2165