Bootstrapping the Stochastic Resonance

TL;DR

This paper rigorously analyzes stochastic resonance in a double-well potential using convex optimization, deriving bounds on the expected signal power enhancement due to noise, advancing theoretical understanding of the phenomenon.

Contribution

It introduces a novel application of convex optimization to derive rigorous bounds in stochastic resonance, providing new theoretical insights.

Findings

Derived two-sided bounds on expected signal power

Applied convex optimization to stochastic resonance analysis

Enhanced theoretical understanding of noise-induced signal amplification

Abstract

Stochastic resonance is a phenomenon where a noise of appropriate intensity enhances the input signal strength. In this work, by employing the recently developed convex optimization methods in the context of dynamical systems and stochastic processes, we derive rigorous two-sided bounds on the expected power at the input signal frequency for the prototypical example of stochastic resonance, the double-well potential with periodic forcing and Gaussian white noise.