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

Lukas Anzeletti; Khoa Lê; Chengcheng Ling

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arXiv · 2304.06802

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

Lukas Anzeletti·Khoa Lê·Chengcheng Ling

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Abstract

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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Lukas Anzeletti, Khoa Lê, Chengcheng Ling. 2023-04-13. Path-by-path uniqueness for stochastic differential equations under Krylov-R\"ockner condition. https://arxiv.org/abs/2304.06802

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