Characterizing stochastic inertia: when does noise increase escape times?
Abstract
Motivated by observations in atmospheric modelling, we investigate the effect of ``stochastic inertia'': in certain dynamical systems, small noise induces trajectories to stay longer in a dynamically critical subset of state space than in the purely deterministic situation. Under mild general assumptions on the stochastic differential equation, we derive an integral formula along deterministic trajectories whose sign provides a sufficient condition for the occurrence of stochastic inertia. Excluding situations with open sets of infinite escape times and assuming uniformly elliptic diffusion, we additionally identify this integral formula as the zero noise derivative of the average escape time. The proofs make crucial use of Dynkin's formula and suitable adaptations of Freidlin--Wentzell theory. We present an algorithmic approach to compute the integral formula and, by examples of saddle points and relaxation oscillators, demonstrate the following heuristic: stochastic inertia appears in the presence of an unstable direction that predominantly leads the escape dynamics.
Related
- Small inertia limit of the distribution-dependent stochastic Cucker--Smale equation
- Linear Response Theory for Jump-Driven Stochastic Systems: Transient Statistics and Escape Dynamics
- Stochastic Two-Dimensional Anisotropic Magnetohydrodynamics System with Multiplicative Noise
- Stochastic fractional diffusion equations with spatial Gaussian noise in the Stratonovich regime
- Continuous stochastic flows driven by white noise and their duals
BibTeX
@misc{chemnitz2026characterizing,
title = {{Characterizing stochastic inertia: when does noise increase escape times?}},
author = {Robin Chemnitz and Maximilian Engel and Péter Koltai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08685},
eprint = {2610.08685},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08685},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Characterizing stochastic inertia: when does noise increase escape times?
AU - Robin Chemnitz
AU - Maximilian Engel
AU - Péter Koltai
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08685
UR - https://arxiv.org/abs/2610.08685
AB - Motivated by observations in atmospheric modelling, we investigate the effect of ``stochastic inertia'': in certain dynamical systems, small noise induces trajectories to stay longer in a dynamically critical subset of state space than in the purely deterministic situation. Under mild general assumptions on the stochastic differential equation, we derive an integral formula along deterministic trajectories whose sign provides a sufficient condition for the occurrence of stochastic inertia. Excluding situations with open sets of infinite escape times and assuming uniformly elliptic diffusion, we additionally identify this integral formula as the zero noise derivative of the average escape time. The proofs make crucial use of Dynkin's formula and suitable adaptations of Freidlin--Wentzell theory. We present an algorithmic approach to compute the integral formula and, by examples of saddle points and relaxation oscillators, demonstrate the following heuristic: stochastic inertia appears in the presence of an unstable direction that predominantly leads the escape dynamics.
ER -