Strong completeness of SDEs and non-explosion for RDEs with coefficients having unbounded derivatives

Abstract

We establish a non-explosion result for rough differential equations (RDEs) in which the noise and drift coefficients, together with their derivatives, may grow unboundedly at infinity. In addition, we prove the existence of a global bi-continuous solution flow for stochastic differential equations (SDEs). Finally, the non-explosion results for RDEs are shown to be sharp by constructing counterexamples.