Proof(s) of the Lamperti representation of continuous-state branching processes

DOI10.1214/09-PS154zbMath1194.60053arXiv0802.2693MaRDI QIDQ980783

Gerónimo Uribe Bravo, Amaury Lambert, Maria-Emilia Caballero

Publication date: 29 June 2010

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.2693

zbMATH Keywords

random time changecontinuous-state branching processesstochastic integral equationsSkorohod topologyspectrally positive Lévy processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Martingales with continuous parameter (60G44) Convergence of probability measures (60B10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Stochastic integral equations (60H20)

Related Items (34)

Extinction properties of multi-type continuous-state branching processes ⋮ Ray-Knight representation of flows of branching processes with competition by pruning of Lévy trees ⋮ Scaling limits of population and evolution processes in random environment ⋮ Continuous-state branching processes with competition: duality and reflection at infinity ⋮ Moments of continuous-state branching processes in Lévy random environments ⋮ Branching Processes -- A General Concept ⋮ An axiomatic characterization of the Brownian map ⋮ A Lamperti-type representation of continuous-state branching processes with immigration ⋮ Scaling limits via excursion theory: interplay between Crump-Mode-Jagers branching processes and processor-sharing queues ⋮ Integral functionals for spectrally positive Lévy processes ⋮ Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property ⋮ Improved Hölder continuity near the boundary of one-dimensional super-Brownian motion ⋮ Extinction times of multitype continuous-state branching processes ⋮ The relative frequency between two continuous-state branching processes with immigration and their genealogy ⋮ Stochastic equations for two-type continuous-state branching processes with immigration ⋮ Lamperti transformation for continuous-state branching processes with competition and applications ⋮ Multilevel Monte Carlo simulation for Lévy processes based on the Wiener-Hopf factorisation ⋮ The genealogy of branching Brownian motion with absorption ⋮ TheW,Zscale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems ⋮ Continuous state branching processes in random environment: the Brownian case ⋮ Branching processes seen from their extinction time via path decompositions of reflected Lévy processes ⋮ Branching processes in a Lévy random environment ⋮ A continuous-state polynomial branching process ⋮ Breadth First Search Coding of Multitype Forests with Application to Lamperti Representation ⋮ Coagulation-transport equations and the nested coalescents ⋮ Self-decomposable laws from continuous branching processes ⋮ Coagulation and universal scaling limits for critical Galton–Watson processes ⋮ The dimension of the boundary of super-Brownian motion ⋮ On a two-parameter Yule-Simon distribution ⋮ Superprocesses as Models for Information Dissemination in the Future Internet ⋮ Growth-fragmentation processes in Brownian motion indexed by the Brownian tree ⋮ Asymptotic behavior of local times of compound Poisson processes with drift in the infinite variance case ⋮ Continuous-state branching processes with spectrally positive migration ⋮ Equivalence of mean-field avalanches and branching diffusions: from the Brownian force model to the super-Brownian motion

This page was built for publication: Proof(s) of the Lamperti representation of continuous-state branching processes