3 papers
math.PR2025
Scaled quadratic variation for controlled rough paths and parameter estimation of fractional diffusions
James-Michael Leahy, Torstein Nilssen
We introduce the concept of finite -scaled quadratic variation along a sequence of partitions for paths on a given interval. This concept, with historical roots in the study of…
math.AP2025
Unbounded rough drivers, rough PDEs and applications
Antoine Hocquet, Martina Hofmanova, Torstein Nilssen
A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present…
math.AP2025
On the well-posedness of (nonlinear) rough continuity equations
Lucio Galeati, James-Michael Leahy, Torstein Nilssen
Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-…