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Path-by-path uniqueness for stochastic differential equations under Krylov-R\"ockner condition

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arxiv 2304.06802 v2 pith:NHLFRJKL submitted 2023-04-13 math.PR math.CA

Lukas Anzeletti , Khoa Lê , Chengcheng Ling This is my paper · ORCID
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We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion. Consequentially, such SDE is strongly complete and forms a random dynamical system. Also, a further application to a boundary value problem is discussed.

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  1. Effective Lagrangian regularity and the uniqueness threshold for random H\"older velocity fields

    math.PR 2026-08 accept novelty 8.0 of 10

    For random multiscale Hölder velocity fields with finite-range dependence, uniqueness of ODE and transport solutions holds almost surely above the sharp threshold alpha=1/2, with explicit counterexamples below.

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