arXiv Analytics

Sign in

arXiv:2111.13795 [math.PR]AbstractReferencesReviewsResources

On strong solutions of Itô's equations with $Dσ$ and $b $ in Morrey classes containing $L_{d}$

N. V. Krylov

Published 2021-11-27, updated 2022-08-17Version 2

We consider It\^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{2+\varepsilon,loc}$, and the drift in a Morrey class containing $L_{d}$. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.

Comments: 24 pages. An important example added. arXiv admin note: text overlap with arXiv:2007.06040
Categories: math.PR, math.AP
Subjects: 60H10, 60J60
Related articles: Most relevant | Search more
arXiv:2007.06040 [math.PR] (Published 2020-07-12)
On strong solutions of Itô's equations with a$\,\in W^{1}_{d}$ and b$\,\in L_{d}$
arXiv:2208.04868 [math.PR] (Published 2022-08-09)
Remarks on the post of Röckner and Zhao about strong solutions of stochastic equations with critical singularities at arXiv:2103.05803v4
arXiv:2207.03626 [math.PR] (Published 2022-07-08)
On strong solutions of time inhomogeneous Itô's equations with "supercritical'' diffusion and drift

Links

Toolbox