Statistical inference from total-mass asymptotics

Determine whether the small-time asymptotics of the renormalized Stratonovich parabolic Anderson model’s total mass can be used to construct meaningful statistical inference procedures for the coupling parameter and the fractional Brownian sheet’s Hurst parameters.

Background

The fluctuations–renormalization phase transition suggests that, in some regimes, the total mass’s small-time behavior may provide consistent estimators for the coupling strength and noise parameters.

The paper explicitly leaves unresolved whether this observation can be developed into statistically meaningful inference methodology, particularly for renormalized Stratonovich equations.

References

We leave the question of whether this can be leveraged into meaningful statistical inference procedures open.

— The Parabolic Anderson Model's Total Mass at Small Times: Geometry, Fluctuations, and Renormalization  (2608.18834 - Lamarre et al., 19 Aug 2026) in Remark, Section 2.3 (The Fluctuations-Renormalization Transition)