Zero noise limits using local times

TL;DR

This paper investigates the zero noise limits of stochastic differential equations with irregular drifts, using local times to identify the trajectories selected in the limit, employing elementary probabilistic methods.

Contribution

It introduces a probabilistic approach using mollified local times to determine the zero noise limit trajectories for SDEs with irregular drifts, providing a new perspective.

Findings

Identifies the zero noise limit trajectories using local times.

Provides a probabilistic and elementary stochastic calculus method.

Clarifies the selection mechanism in irregular drift SDEs.

Abstract

We consider a well-known family of SDEs with irregular drifts and the correspondent zero noise limits. Using (mollified) local times, we show which trajectories are selected. The approach is completely probabilistic and relies on elementary stochastic calculus only.