Benedetta Ferrario

Ergodic results for stochastic navier-stokes equation

In this paper we deal with the 2-D Navier-Stokes equation perturbed by a white noise force. Uniqueness of the invariant measure for this stochastic equation is obtained in a simpler way than in [6], proving that the two main properties of the Markov semigroup associated with this equation, i.e. irreducibility and strong Feller property, hold in the same space. Moreover, the assumptions on the noise are more general than in [6]

Backward Stochastic Differential Equations driven by càdlàg martingales

Backward stochastic differential equations (BSDEs) arise in many financial problems. Although there exists a growing number of papers considering general financial markets, the theory of BSDEs has been developed just in the Brownian setting. We consider BSDEs driven by an

Stochastic Navier-Stokes equations: Analysis of the noise to have a unique invariant measure

{\bf R}^d

The Bénard problem with random perturbations: dissipativity and invariant measures

-valued cadlag martingale and we study the properties of the solutions in the case of a, possibly nonuniform, Lipschitz generator.

UNIQUENESS OF SOLUTIONS OF THE STOCHASTIC NAVIER-STOKES EQUATION WITH INVARIANT MEASURE GIVEN BY THE ENSTROPHY

In [6], it has been proven that there exists a unique invariant measure for the 2D Navier-Stokes equations perturbed by a white noise term; this is the probability measure representing the asymptotic behavior. There, the assumptions on the noise were quite restrictive. In this paper we remove the heaviest limitation, that is the lower bound on the range of the noise covariance, providing a complete analysis of sufficient conditions for the existence of a unique invariant measure.

Inviscid limit of stochastic damped 2D Navier–Stokes equations

Abstract. We consider the Navier-Stokes equations perturbed by white noise, coupled with the heat equation. We prove an existence and uniqueness result for the solution and the existence of invariant measures for the associated semigroup.

A stochastic model of seed dispersal pattern to assess seed predation by ants in annual dry grasslands

A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure μ ν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for μ ν -a.e. initial velocity is proven for solutions having μ ν as invariant measure.

On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The rates are computed with respect to a limit measure of the unique invariant measure of the stochastic damped Navier-Stokes equations.

A Note on a Result of Liptser-Shiryaev

A combined field experiment and modelling approach has been used to provide evidence that ants may be responsible for an observed lower patchiness and higher plant diversity in the neighbourhood of ant nests, within Mediterranean dry grasslands belonging to the phytosociological class Tuberarietea guttatae. The hypothesis was that seeds occurring in clumps may have a higher probability to be harvested than seeds having a scattered distribution. In order to test this hypothesis, four analysis steps were performed. First, pattern of seed production and dispersal of four species was recorded; two of them were more abundant next to ant nests (Tuberaria guttata, Euphorbia exigua), whereas the other two were more abundant away from ant nests (Bromus scoparius and Plantago bellardi). Second, a stochastic model was developed to simulate the observed dispersal patterns of each studied species. Third, 10 seed spatial arrangements in accordance to the distribution patterns created by the model were offered to ants and the location of predated seeds was recorded. Finally, the observed pattern of seed predation was matched to models performed by different distributions of probability. Results showed that the probability of being predated decreased as distance among seeds increased. This preference of ants for high concentration of food items holds down the dominant species sufficiently to allow the subordinates to survive, thus increasing diversity near nests. The observed higher frequency of small-seeded, small-sized, or creeping therophytes close to the ant nests can be therefore seen as an example of indirect myrmecophily.

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

The essential self-adjointness on a natural domain of the sharp-time Wick powers of the relativistic free field in two space-time dimension is proven. Other results on Wick powers are reviewed and discussed.