On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees

zbMath1414.60022arXiv1706.03495MaRDI QIDQ4962126

Robin Stephenson

Publication date: 30 October 2018

Full work available at URL: https://arxiv.org/abs/1706.03495

zbMATH Keywords

Lévy processesHausdorff dimensionexponential functionalrandom treesfragmentation processesMarkov additive processes

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Continuous-time Markov processes on general state spaces (60J25) Self-similar stochastic processes (60G18) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Exchangeability for stochastic processes (60G09)

Related Items (12)

Bivariate Markov chains converging to Lamperti transform Markov additive processes ⋮ Exponential functionals of Markov additive processes ⋮ Stability of overshoots of Markov additive processes ⋮ Growing random graphs with a preferential attachment structure ⋮ Self-similar signed growth-fragmentations ⋮ Entrance laws at the origin of self-similar Markov processes in high dimensions ⋮ Asymptotic results for heavy-tailed Lévy processes and their exponential functionals ⋮ Scaling limits of multi-type Markov branching trees ⋮ Stable Lévy processes in a cone ⋮ Fragmentations with self-similar branching speeds ⋮ On the finiteness and tails of perpetuities under a Lamperti–Kiu MAP ⋮ Unnamed Item

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