Consider a general class of branching Markov processes with non-local offspring distribution, or a non-local general superprocess. Let k be a non-negative integer. We will show that, when the mean semigroup possesses a Perron-Frobenius type asymptotic decomposition, remarkably precise asymptotic growth results for its k-th moments and the k-th moments of its occupation measure can be established as t -> oo.

The method relies on a combinatorial decomposition of the moments, correctly identifying and treating the leading order terms and using ergodic properties that follow as a result of the Perron-Frobenius assumption.

This is joint work with Emma Horton and Isaac Gonzalez.