Uniqueness of strong solutions for SDEs with H\"older diffusions

This paper is concerned with the It\^o stochastic differential equations with $\mR^{d\times k}$ diffusions in class of H\"older spaces and continuous $\mR^d$ drifts. We derive a uniqueness result of strong solutions for $\cC^\alpha \ (\alpha\geq \frac{1}{2})$ coefficients and this result is new. Our proof is supported by It\^o's formula and a finer analysis on cut-off and smoothing techniques.