Bivariate Markov chains converging to Lamperti transform Markov additive processes

DOI10.1016/j.spa.2017.11.008zbMath1409.60107arXiv1612.06058OpenAlexW2595579455MaRDI QIDQ1615902

Robin Stephenson, Bénédicte Haas

Publication date: 31 October 2018

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

Full work available at URL: https://arxiv.org/abs/1612.06058

zbMATH Keywords

Lamperti transformGalton-Watson treesbivariate Markov chains

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Self-similar stochastic processes (60G18) Functional limit theorems; invariance principles (60F17)

Related Items

Scaling Limits of Markov-Branching Trees and Applications, Scaling limits of multi-type Markov branching trees

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-similar scaling limits of Markov chains on the positive integers
• Inversion, duality and Doob \(h\)-transforms for self-similar Markov processes
• On the number of collisions in beta(\(2, b\))-coalescents
• Self-similar scaling limits of non-increasing Markov chains
• Scaling limits of Markov branching trees with applications to Galton-Watson and random unordered trees
• Scaling limits of \(k\)-ary growing trees
• Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic mod\-els
• On the number of collisions in lambda-coalescents
• On the Markov renewal theorem
• Coalescents with multiple collisions
• Random planar maps and growth-fragmentations
• The coalescent in population models with time-inhomogeneous environment.
• Fires on trees
• The Lamperti representation of real-valued self-similar Markov processes
• The hitting time of zero for a stable process
• Renewal approximation for the absorption time of a decreasing Markov chain
• On Λ-Coalescents with Dust Component
• Recent progress in coalescent theory
• Applied Probability and Queues
• Semi-Stable Stochastic Processes
• The general coalescent with asynchronous mergers of ancestral lines
• On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees
• Semi-stable Markov processes. I
• On the number of jumps of random walks with a barrier
• On Asymptotics of Exchangeable Coalescents with Multiple Collisions
• The height of increasing trees