Intermittency and Aging for the Symbiotic Branching Model

TL;DR

This paper investigates how aging and intermittency behave differently depending on correlation signs in the symbiotic branching model, offering new proofs and refinements for related stochastic processes.

Contribution

It provides an alternative elementary proof and extends classical results on second moments and aging phenomena in related stochastic models.

Findings

Aging and intermittency differ for negative, zero, and positive correlations.

New elementary proof for classical second moment results.

Refinements for aging in models with general kernels.

Abstract

For the symbiotic branching model introduced by Etheridge/Fleischmann (2004), it is shown that aging and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with Brownian potential. Some refinements to more general (also infinite range) kernels of recent aging results of Dembo/Deuschel (2007) for interacting diffusions are given.