Fluctuation limits of strongly degenerate branching systems

TL;DR

This paper establishes functional limit theorems for scaled fluctuations of occupation times in critical, anisotropic branching particle systems with degenerate splitting, revealing limit processes as constant measure-valued Wiener processes.

Contribution

It introduces new limit theorems for occupation time fluctuations in strongly degenerate, anisotropic branching systems, extending understanding of their asymptotic behavior.

Findings

Limit processes are constant measure-valued Wiener processes.

Results apply to critical and intermediate dimensions.

Limit processes exhibit degenerated temporal and simple spatial structures.

Abstract

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ 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.