Riemann-Liouville processes arising from Branching particle systems

TL;DR

This paper demonstrates that Riemann-Liouville processes can emerge from the scaled occupation time fluctuations of certain site-dependent branching particle systems under specific conditions.

Contribution

It establishes a novel connection between Riemann-Liouville processes and the temporal structure of occupation time fluctuations in branching particle systems.

Findings

Riemann-Liouville processes arise from scaled occupation time limits.

The result applies to systems with 1=d<α<2 and finite integral of σ(x).

Provides a new perspective on the stochastic structure of branching systems.

Abstract

It is proved in this paper that Riemann-Liouville processes can arise from the temporal structures of the scaled occupation time fluctuation limits of the site-dependent (d,\alpha,\sigma(x))branching particle systems in the case of 1=d<\alpha<2 and \int_{\R}\sigma(x)\d x<\infty.