Fluctuation limits of strongly degenerate branching systems

Abstract

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in ${\mathbb{R}}^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.

15 pages

References in corpus (4)

• 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
• Occupation time fluctuations of an infinite variance branching system in large dimensions
• Occupation Time Fluctuations of Weakly Degenerate Branching Systems

Cited by in corpus (1)

• Riemann-Liouville processes arising from Branching particle systems