Rough differential equations with unbounded drift term

2016/05/18 by Riedel, Sebastian, Scheutzow, Michael · 2 citations
#34A34 #34F05 #60G15 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1605.05604

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.

Cited by

• Averaging principle for slow-fast systems of PDEs with rough drivers
• Rough stochastic filtering

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