Uniqueness of strong solutions for SDEs with Hölder diffusions

Abstract

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

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