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arXiv · 2402.12703

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

Yuanhang Liu·Donghui Yang·Xingwu Zeng·Can Zhang
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Abstract

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.

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Yuanhang Liu, Donghui Yang, Xingwu Zeng, Can Zhang. 2024-02-20. Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space. https://arxiv.org/abs/2402.12703

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