Author

Mauricio-René Herrera-Marín

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Preprint Sep 2026

Learning the exogenous rate but not the distance to criticality in nearly unstable heavy-tailed Hawkes processes

In the nearly unstable heavy-tailed regime of Jaisson and Rosenbaum, where the intensity of a linear Hawkes process converges to a rough square-root Volterra process, we ask what a record of length $T$ reveals about the relative distance to criticality $1-\rho$ and the exogenous rate $\mu$. For the first, the informati...

Mauricio-René Herrera-Marín · 0 citations

Preprint Sep 2026

Minimax and adaptive inference for branching ratios under long memory

The branching ratio $\rho$ of a self-exciting point process determines the branching margin $1-\rho$ to the critical boundary. We study inference on $\rho$ from a finite record for stationary Hawkes processes with completely monotone kernels whose slow relaxation mass obeys an envelope near zero rate. Slow excitation c...

Mauricio-René Herrera-Marín · 1 citation

#machine learning Preprint Sep 2026

Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics

Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fractional Laplace neural operator (fLNO) that embeds this structure in the learned map. For commuting excitation--Laplacian pairs, one block grap...

Mauricio-René Herrera-Marín · 0 citations