A result on power moments of L\'evy-type perpetuities and its application to the $L_p$-convergence of Biggins' martingales in branching L\'evy processes
From MaRDI portal
Publication:4623163
zbMath1406.60063arXiv1811.08721MaRDI QIDQ4623163
Bastien Mallein, Aleksander M. Iksanov
Publication date: 14 February 2019
Full work available at URL: https://arxiv.org/abs/1811.08721
\(L_p\)-convergencespinal decompositionbranching Lévy processBiggins' martingaleLévy-type perpetuity
Processes with independent increments; Lévy processes (60G51) Martingales with continuous parameter (60G44) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
Related Items
On the law of terminal value of additive martingales in a remarkable branching stable process, A necessary and sufficient condition for the convergence of the derivative martingale in a branching Lévy process
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The many-to-few lemma and multiple spines
- On distributional properties of perpetuities
- Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
- Measure changes with extinction
- A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks
- On generalized multiplicative cascades
- Martingales in self-similar growth-fragmentations and their connections with random planar maps
- Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the \(M_1\)-topology
- Stability of perpetuities
- Conceptual proofs of \(L\log L\) criteria for mean behavior of branching processes
- A renewal theorem and supremum of a perturbed random walk
- Biggins' martingale convergence for branching Lévy processes
- Infinitely ramified point measures and branching Lévy processes
- Elementary fixed points of the BRW smoothing transforms with infinite number of summands
- Stochastic Models with Power-Law Tails
- Renewal Theory for Perturbed Random Walks and Similar Processes
- Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise
- Exponential moments of first passage times and related quantities for Lévy processes
- Martingale convergence in the branching random walk
- Null recurrence and transience of random difference equations in the contractive case
- Functional limit theorems for the number of busy servers in a G/G/∞ queue
- On perpetuities with gamma-like tails
- Measure change in multitype branching
