Author: Barczy, Mátyás; Nedényi, Fanni K.; Pap, Gyula
Title: On Aggregation of Subcritical Galton–Watson Branching Processes with Regularly Varying Immigration Cord-id: qf4exhuj Document date: 2020_9_17
ID: qf4exhuj
Snippet: Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching process with regularly varying immigration having index α ∈ (0, 2). We show that limits of finite-dimensional distributions of appropriately centered and scaled aggregated partial-sum processes exist when first taking the limit as N → ∞and then the time scale n→ ∞. The limit process is an α-stable process if α ∈ (0, 1) ∪ (
Document: Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching process with regularly varying immigration having index α ∈ (0, 2). We show that limits of finite-dimensional distributions of appropriately centered and scaled aggregated partial-sum processes exist when first taking the limit as N → ∞and then the time scale n→ ∞. The limit process is an α-stable process if α ∈ (0, 1) ∪ (1, 2) and a deterministic line with slope 1 if α = 1.
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