Strong Uniqueness of Degenerate SDEs with H\"older diffusion coefficients

TL;DR

This paper establishes new strong uniqueness and weak existence results for degenerate multidimensional SDEs with Sobolev and H"older diffusion coefficients, broadening understanding of such stochastic systems.

Contribution

It introduces novel strong uniqueness and weak existence theorems for degenerate SDEs with Sobolev and H"older diffusion coefficients, including concrete examples.

Findings

Proved strong uniqueness for degenerate SDEs with Sobolev diffusion.

Established weak existence results under rough drift conditions.

Provided examples with H"older diffusion coefficients.

Abstract

In this paper we prove a new strong uniqueness result and a weak existence result for possibly {\it degenerate} multidimensional stochastic differential equations with Sobolev diffusion coefficients and rough drifts. In particular, examples with H\"older diffusion coefficients are provided to show our results.