Continuous state branching processes in random environment: the Brownian case

DOI10.1016/j.spa.2016.07.006zbMath1355.60049arXiv1506.09197OpenAlexW2963756592MaRDI QIDQ511139

Sandra Palau, Juan Carlos Pardo

Publication date: 14 February 2017

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

Full work available at URL: https://arxiv.org/abs/1506.09197

zbMATH Keywords

Brownian motionQ-processcontinuous state branching processes in random environmentcontinuous state branching processes with immigration in random environmentexplosion and extinction probabilitiesexponential functional of Brownian motionsupercritical process conditioned on eventual extinction

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sample path properties (60G17) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

• On the extinction of continuous state branching processes with catastrophes
• Stochastic equations, flows and measure-valued processes
• Supercritical branching diffusions in random environment
• Exponential functionals of Lévy processes
• Proof(s) of the Lamperti representation of continuous-state branching processes
• Continuous branching processes and spectral positivity
• Theory of stochastic differential equations with jumps and applications.
• Stochastic equations of non-negative processes with jumps
• Fluctuations of Lévy processes with applications. Introductory lectures
• Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct
• Properties of perpetual integral functionals of Brownian motion with drift
• On the scaling limits of Galton-Watson processes in varying environments
• Branching diffusions in random environment
• On Prolific Individuals in a Supercritical Continuous-State Branching Process
• The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
• Asymptotic behaviour of continuous time, continuous state-space branching processes
• On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts
• Continuous-State Branching Processes and Self-Similarity
• Stochastic branching processes with continuous state space
• Continuous state branching processes
• Unnamed Item
• Unnamed Item

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