Limit theorems for Smoluchowski dynamics associated with critical continuous-state branching processes

DOI10.1214/14-AAP1008zbMath1312.60100arXiv1212.6451MaRDI QIDQ2341629

Robert L. Pego, Nicholas Leger, Gautam Iyer

Publication date: 27 April 2015

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

Full work available at URL: https://arxiv.org/abs/1212.6451

zbMATH Keywords

regular variationscaling limitself-similar solutioncoagulationSmoluchowski equationBernstein functioncontinuous-state branching processcritical branchingMittag-Leffler series

Mathematics Subject Classification ID

Self-similar stochastic processes (60G18) Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics (82C28) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) PDEs in connection with mechanics of particles and systems of particles (35Q70)

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Cites Work

• Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
• Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations
• Universality classes in Burgers turbulence
• The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations
• Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct
• Introductory lectures on fluctuations of Lévy processes with applications.
• Stochastic flows associated to coalescent processes. III: Limit theorems
• Critical markov branching process limit theorems allowing infinite variance
• Asymptotic behaviour of continuous time, continuous state-space branching processes
• Renormalization group and asymptotics of solutions of nonlinear parabolic equations
• Approach to self‐similarity in Smoluchowski's coagulation equations
• Continuous-State Branching Processes and Self-Similarity
• Further notes on branching processes with mean 1
• Measure and integration theory. Transl. from the German by Robert B. Burckel
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