Strong solutions of stochastic differential equations with coefficients in mixed-norm spaces

TL;DR

This paper establishes the existence and uniqueness of strong solutions for stochastic differential equations with coefficients in mixed-norm spaces, extending previous results by Krylov, R"ockner, and Zhang.

Contribution

It introduces a new approach to handle coefficients in mixed-norm spaces for stochastic differential equations, broadening the class of equations with known strong solutions.

Findings

Proves existence of strong solutions in mixed-norm coefficient spaces.

Establishes uniqueness of solutions under new conditions.

Extends classical results to more general coefficient spaces.

Abstract

By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of strong solutions to stochastic differential equations driven by Brownian motion with coefficients in spaces with mixed-norm, which extends Krylov and R\"ockner's result in [11] and Zhang's result in [18].