arXiv subjects

Benedetta Ferrario

Publications and source records attributed to Benedetta Ferrario.

21 records · Page 2Linked to original sources

arXiv2011

2D hydrodynamical systems: invariant measures of Gaussian type

Gaussian measures $μ^{β,ν}$ are associated to some stochastic 2D hydrodynamical systems. They are of Gibbsian type and are constructed by means of some invariant quantities of the system depending on some parameter $β$ (related to the 2D nature of the fluid) and the viscosity $ν$. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure $μ^{β,ν}$ is invariant for this flow and is unique. Finally, we prove that the deterministic inviscid equation has a $μ^{β,ν}$-stationary solution (for any $ν>0$).

math.PR↗

arXiv2011

Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases

Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model and a global flow for the deterministic inviscid shell model, with the property that these Gibbs measures are invariant for these flows.

math-ph↗

arXiv2010

A note on a result of Liptser-Shiryaev

Given two stochastic equations with different drift terms, under very weak assumptions Liptser and Shiryaev provide the equivalence of the laws of the solutions to these equations by means of Girsanov transform. Their assumptions involve both the drift terms. We are interested in the same result but with the main assumption involving only the difference of the drift terms. Applications of our result will be presented in the finite as well as in the infinite dimensional setting.

math.PR↗