Implicit renewal theorem for trees with general weights

DOI10.1016/J.SPA.2012.05.004zbMath1258.60040arXiv1012.2165OpenAlexW2067952159MaRDI QIDQ444354

Mariana Olvera-Cravioto, Predrag R. Jelenković

Publication date: 14 August 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2165

zbMATH Keywords

power lawsimplicit renewal theoremweighted branching processesdistributional fixed-point equationssmoothing transforms

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Renewal theory (60K05)

Related Items (21)

Importance sampling for maxima on trees ⋮ The fixed points of the multivariate smoothing transform ⋮ On fixed points of a generalized multidimensional affine recursion ⋮ PageRank in Scale-Free Random Graphs ⋮ Fixed points of the smoothing transform: two-sided solutions ⋮ Regularly log-periodic functions and some applications ⋮ Heavy tailed solutions of multivariate smoothing transforms ⋮ Maximums on trees ⋮ Robustness of power-law behavior in cascading line failure models ⋮ PageRank on inhomogeneous random digraphs ⋮ PageRank's behavior under degree correlations ⋮ Convergence Rates in the Implicit Renewal Theorem on Trees ⋮ Implicit renewal theory in the arithmetic case ⋮ Convergence of the population dynamics algorithm in the Wasserstein metric ⋮ Stationary Waiting Time in Parallel Queues with Synchronization ⋮ Limit theorems for branching processes with immigration in a random environment ⋮ The Smoothing Transform: A Review of Contraction Results ⋮ Precise Tail Index of Fixed Points of the Two-Sided Smoothing Transform ⋮ Precise tail asymptotics of fixed points of the smoothing transform with general weights ⋮ Distribution of the Number of Retransmissions of Bounded Documents ⋮ Staffing Many-Server Systems with Admission Control and Retrials

Cites Work

• Unnamed Item
• A survey of max-type recursive distributional equations
• The functional equation of the smoothing transform
• Implicit renewal theory and tails of solutions of random equations
• A stochastic fixed point equation related to weighted branching with deterministic weights
• Random difference equations and renewal theory for products of random matrices
• Sur certaines martingales de Benoit Mandelbrot
• One limit distribution for a random walk on the line
• Seneta-Heyde norming in the branching random walk
• On generalized multiplicative cascades
• A general limit theorem for recursive algorithms and combinatorial structures
• The contraction method for recursive algorithms
• Fixed points of the smoothing transform: two-sided solutions
• Elementary fixed points of the BRW smoothing transforms with infinite number of summands
• Tail Asymptotics for the Busy Period in the GI/G/1 Queue
• Approximating the limiting Quicksort distribution
• Implicit Renewal Theory and Power Tails on Trees
• Information ranking and power laws on trees
• Asymptotic analysis for personalized Web search
• Generalized potlatch and smoothing processes
• Martingale convergence in the branching random walk
• Fixed points of a generalized smoothing transformation and applications to the branching random walk
• Fixed points of the smoothing transformation
• The matrix analogue of the Blackwell renewal theorem on the real line

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