Noise reinforcement for Lévy processes

DOI10.1214/19-AIHP1037zbMath1477.60069arXiv1810.08364MaRDI QIDQ2227484

Jean Bertoin

Publication date: 15 February 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.08364

zbMATH Keywords

Lévy processBlumenthal-Getoor indexpreferential attachmentreinforcementYule-Simon distribution

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (10)

Multidimensional walks with random tendency ⋮ Scaling exponents of step-reinforced random walks ⋮ The enhanced strong invariance principle for the elephant random walk ⋮ On the local times of noise reinforced Bessel processes ⋮ Noise reinforced Lévy processes: Lévy-Itô decomposition and applications ⋮ Universality of noise reinforced Brownian motions ⋮ Reinforced random walks under memory lapses ⋮ Gaussian fluctuation for superdiffusive elephant random walks ⋮ Joint invariance principles for random walks with positively and negatively reinforced steps ⋮ Functional limit theorems for the multi-dimensional elephant random walk

Cites Work

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• Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
• A survey of random processes with reinforcement
• The shark random swim. (Lévy flight with memory)
• Transience of edge-reinforced random walk
• Edge- and vertex-reinforced random walks with super-linear reinforcement on infinite graphs
• Localization for linearly edge reinforced random walks
• ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS
• Criteria for the finiteness of the strong p-variation for Lévy-type processes
• A martingale approach for the elephant random walk
• Random walks with preferential relocations and fading memory: a study through random recursive trees
• Central limit theorem and related results for the elephant random walk

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