Parabolic equations and SDEs with time-inhomogeneous Morrey drift

D. Kinzebulatov

Parabolic equations and SDEs with time-inhomogeneous Morrey drift

Probability 2023-03-08 v2 Analysis of PDEs

Authors: D. Kinzebulatov

Abstract

We prove the unique weak solvability of stochastic differential equations with time-inhomogeneous drift in essentially the largest (scaling-invariant) Morrey class, i.e.\,with integrability parameter $q>1$ close to $1$ . The constructed weak solutions constitute a Feller evolution family. The proofs are based on a detailed Sobolev regularity theory of the corresponding parabolic equation.

Keywords

stochastic differential equations time-inhomogeneous drift morrey class weak solvability feller evolution family parabolic equation sobolev regularity

Cite

@article{arxiv.2301.13805,
  title  = {Parabolic equations and SDEs with time-inhomogeneous Morrey drift},
  author = {D. Kinzebulatov},
  journal= {arXiv preprint arXiv:2301.13805},
  year   = {2023}
}

Comments

Fixed a minor error in one of the definitions, added another uniqueness result, updated references

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