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arXiv · 2012.04161

SDEs with critical time dependent drifts: weak solutions

Michael Röckner·Guohuan Zhao
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Abstract

We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T]; L^{p}(\mathbb{R}^d))$ with $d/p+2/q=1$. The weak uniqueness is obtained by solving corresponding Kolmogorov's backward equations in some second order Sobolev spaces, which is analytically interesting in itself.

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Michael Röckner, Guohuan Zhao. 2020-12-08. SDEs with critical time dependent drifts: weak solutions. https://arxiv.org/abs/2012.04161

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