Browsing AURA by Author "Nilssen, Torstein"
Now showing items 1-8 of 8
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Geometric rough paths on infinite dimensional spaces
Grong, Erlend; Nilssen, Torstein; Schmeding, Alexander (Peer reviewed; Journal article, 2022)Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For α ∈ (1/3,1/2), we give criteria for when we can approximate Banach space-valued ... -
Girsanov theorem for multifractional Brownian processes
Harang, Fabian; Nilssen, Torstein; Proske, Frank Norbert (Peer reviewed; Journal article, 2022) -
Girsanov theorem for multifractional Brownian processes
Harang, Fabian Andsem; Nilssen, Torstein; Proske, Frank Norbert (Peer reviewed; Journal article, 2022) -
An Itô Formula for rough partial differential equations and some applications
Hocquet, Antoine; Nilssen, Torstein (Peer reviewed; Journal article, 2020)We investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form ∂tu−Atu−f = (X˙t(x)·∇+Y˙ t(x))u on [0, T ]×Rd . To do so, we introduce a concept of “differential rough driver”, ... -
Random dynamical system generated by the 3D Navier-Stokes equation with rough transport noise
Cardona, Jorge; Hofmanová, Martina; Nilssen, Torstein; Rana, Nimit (Peer reviewed; Journal article, 2022)We consider the Navier-Stokes system in three dimensions perturbed by a transport noise which is sufficiently smooth in space and rough in time. The existence of a weak solution was proved in [26], however, as in the ... -
Rough linear PDEs with discontinuous coefficients – existence of solutions via regularization by fractional Brownian motion
Nilssen, Torstein (Peer reviewed; Journal article, 2020)We consider two related linear PDE’s perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown ... -
Solution properties of the incompressible Euler system with rough path advection
Crisan, Dan; Holm, Darryl D.; Leahy, James-Michael; Nilssen, Torstein (Peer reviewed; Journal article, 2022)The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian ... -
Variational principles for fluid dynamics on rough paths
Crisan, Dan; Holm, Darryl D.; Leahy, James-Michael; Nilssen, Torstein (Peer reviewed; Journal article, 2022)