The zero-noise limit of SDEs with L^∞ drift

2022/05/30 by Fjordholm, Ulrik Skre, Musch, Markus, Pilipenko, Andrey
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2205.15082

Abstract

We study the zero-noise limit for autonomous, one-dimensional ordinary differential equations with discontinuous right-hand sides. Although the deterministic equation might have infinitely many solutions, we show, under rather general conditions, that the sequence of stochastically perturbed solutions converges to a unique distribution on classical solutions of the deterministic equation. We provide several tools for computing this limit distribution.

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