Strong solutions to degenerate SDEs and uniqueness for degenerate Fokker-Planck equations

2024/09/25 by Sebastian Grube, Grube, Sebastian · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #Gas Dynamics and Kinetic Theory #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2409.17135

Abstract

We prove the existence of probabilistically strong solutions for large classes of possibly degenerate stochastic differential equations with locally Sobolev-regular coefficients, using the restricted Yamada-Watanabe theorem. Our approach relies on existence results for the corresponding Fokker-Planck equation, combined with both novel and existing restricted pathwise uniqueness results for SDEs. Here, restricted pathwise uniqueness means pathwise uniqueness among a subclass of weak solutions to the SDE. Furthermore, we derive new uniqueness results for the Fokker-Planck equation.

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