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Integrability properties of (classical, linear, linear growth) roughdifferential equations (RDEs) are considered, the Jacobian of the RDE flowdriven by Gaussian signals being a motivating example. We revisit and extendsome recent ground-breaking work of Cass-Litterer-Lyons in this regard; asby-product, we obtain a user-friendly "transitivity property" of suchintegrability estimates. We also consider rough integrals; as a novelapplication, uniform Weibull tail estimates for a class of (random) roughintegrals are obtained. A concrete example arises from the stochasticheat-equation, spatially mollified by hyper-viscosity, and we can recover (infact: sharpen) a technical key result of [Hairer,Comm.PureAppl.Math.64,no.11,(2011),1547-1585].

Integrability of (non-)linear rough differential equations and integrals