Rough differential equations with unbounded drift term

By Sebastian Riedel, M. Scheutzow. 2016

48 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7db652b805fa11081d011d2bbee0a0031fca1c2

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Citations in the corpus

• Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, methodology): “Using the flow method, the solution to the RDE with unbounded drift term is obtaind by Riedel and Scheutzow [28].”