Second-order asymptotics for the block counting process in a class of regularly varying \({\Lambda}\)-coalescents

DOI10.1214/13-AOP902zbMath1327.60143arXiv1304.5183MaRDI QIDQ2352758

Anna Talarczyk, Vlada Limic

Publication date: 6 July 2015

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.5183

zbMATH Keywords

stable Lévy processPoisson random measuresecond-order asymptotics\({\Lambda}\)-coalescentOrnstein-Uhlenbeck-type SDE

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Continuous-time Markov processes on general state spaces (60J25) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Population dynamics (general) (92D25) Random measures (60G57) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (9)

On the explosion of the number of fragments in simple exchangeable fragmentation-coagulation processes ⋮ On the boundary classification of \(\Lambda\)-Wright-Fisher processes with frequency-dependent selection ⋮ Scaling limits for a class of regular \(\Xi\)-coalescents ⋮ The joint fluctuations of the lengths of the \(\operatorname{Beta}(2 - {\alpha}, {\alpha})\)-coalescents ⋮ Large-scale behaviour and hydrodynamic limit of beta coalescents ⋮ Population dynamics and statistical physics in synergy. Abstracts from the workshop held March 6--12, 2022 ⋮ Scaling limits for the block counting process and the fixation line of a class of $\Lambda$-coalescents ⋮ Λ-coalescents: a survey ⋮ A phase transition in the coming down from infinity of simple exchangeable fragmentation-coagulation processes

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