Limit theorems for occupation time fluctuations of branching systems. II: Critical and large dimensions

DOI10.1016/j.spa.2005.07.004zbMath1089.60021OpenAlexW1979827488MaRDI QIDQ2576955

Anna Talarczyk, Tomasz Bojdecki, Louis G. Gorostiza

Publication date: 29 December 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2005.07.004

zbMATH Keywords

functional limit theoremcritical dimensionbranching particle systemoccupation time fluctuationgeneralized Wiener process

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Self-similar stochastic processes (60G18) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Functional limit theorems; invariance principles (60F17)

Related Items (24)

Functional central limit theorems for supercritical superprocesses ⋮ OCCUPATION TIMES OF SUBCRITICAL BRANCHING IMMIGRATION SYSTEMS WITH MARKOV MOTION, CLT AND DEVIATION PRINCIPLES ⋮ A long range dependence stable process and an infinite variance branching system ⋮ Oscillatory fractional Brownian motion ⋮ Occupation time fluctuations of weakly degenerate branching systems ⋮ Fluctuation limits of strongly degenerate branching systems ⋮ From intersection local time to the Rosenblatt process ⋮ Particle picture interpretation of some Gaussian processes related to fractional Brownian motion ⋮ Fluctuation limits of site-dependent branching systems in critical and large dimensions ⋮ A central limit theorem for branching Brownian motion with random immigration ⋮ A functional ergodic theorem for the occupation time process of a branching system ⋮ Central limit theorems for supercritical branching Markov processes ⋮ A functional CLT for the occupation time of a state-dependent branching random walk ⋮ Occupation time limits of inhomogeneous Poisson systems of independent particles ⋮ Self-similar stable processes arising from high-density limits of occupation times of particle systems ⋮ Some long-range dependence processes arising from fluctuations of particle systems ⋮ Occupation times of subcritical branching immigration systems with Markov motions ⋮ Random systems in ultrametric spaces ⋮ A large deviation for occupation time of critical branching \(\alpha \)-stable process ⋮ OCCUPATION TIME FLUCTUATION LIMITS OF INFINITE VARIANCE EQUILIBRIUM BRANCHING SYSTEMS ⋮ RIEMANN–LIOUVILLE PROCESSES ARISING FROM BRANCHING PARTICLE SYSTEMS ⋮ On the weak convergence of super-Brownian motion with immigration ⋮ A CLASS OF FRACTIONAL BROWNIAN FIELDS FROM BRANCHING SYSTEMS AND THEIR REGULARITY PROPERTIES ⋮ Limit theorems for occupation time fluctuations of branching systems. I: long-range dependence

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