Exponential Wake-Up Overshoot in Explicit Gaussian Point-Process Filters

arXiv:2610.35958v1 Announce Type: new Abstract: When events resume after a long silence, explicit Gaussian point-process filters amplify the first update exponentially in the silence duration. We give the exact distribution of this update and a computable index that predicts when it overshoots. For the explicit (single-scoring-step) filter and its implicit posterior-mode counterpart, we derive second-order silence expansions of the state variance with opposite-sign logarithmic corrections. The crossing index determines when the post-wake prediction exceeds the resumed rate, separating the bin width at which the amplification exponent reaches one from the larger width at which the true rate is overshot.