The zero-noise limit of SDEs with $L^\infty$ drift

Ulrik Skre Fjordholm; Markus Musch; Andrey Pilipenko

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arXiv · 2205.15082

The zero-noise limit of SDEs with $L^\infty$ drift

Ulrik Skre Fjordholm·Markus Musch·Andrey Pilipenko

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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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BibTeX RIS

Ulrik Skre Fjordholm, Markus Musch, Andrey Pilipenko. 2022-05-30. The zero-noise limit of SDEs with $L^\infty$ drift. https://arxiv.org/abs/2205.15082

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