M. Caruana

most citedPartial differential equations driven by rough paths

7 citations · 7 across the 1 of their papers we have counts for

collaborators

2 papers

math.AP2009

A (rough) pathwise approach to a class of non-linear stochastic partial differential equations

Michael Caruana, Peter Friz, Harald Oberhauser

We consider nonlinear parabolic evolution equations of the form $\partial_{t} u = F (t, x, D u, D^{2} u)$ , subject to noise of the form $H (x, D u) \circ d B$ where $H$ is linear in $D u$ and $…

math.AP2008★ 7 cited

Partial differential equations driven by rough paths

Michael Caruana, Peter Friz

We study a class of linear first and second order partial differential equations driven by weak geometric $p$ -rough paths, and prove the existence of a unique solution for these eq…