Path-by-path uniqueness for stochastic differential equations under Krylov-Röckner condition

2023/04/13 by Lukas Anzeletti, Anzeletti, Lukas, Khoa Lê +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60H10 #60H50 #60J60 #Classical Analysis and ODEs (math.CA) #Complex Systems and Time Series Analysis #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2304.06802

openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-Röckner 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.

Citations

• Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation

Cited by

• Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach

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