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arXiv · 1605.05604

Rough differential equations with unbounded drift term

Sebastian Riedel·Michael Scheutzow
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Abstract

We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly. Furthermore, we show that the semiflow exists assuming only appropriate one-sided growth conditions. We provide bounds for both the flow and the semiflow. Applied to stochastic analysis, our results imply "strong completeness" and the existence of a stochastic (semi)flow for a large class of stochastic differential equations. If the driving process is Gaussian, we can further deduce (essentially) sharp tail estimates for the (semi)flow and a Freidlin-Wentzell-type large deviation result.

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Sebastian Riedel, Michael Scheutzow. 2016-05-18. Rough differential equations with unbounded drift term. https://arxiv.org/abs/1605.05604

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