20 research outputs found
On The L{2}-Solutions of Stochastic Fractional Partial Differential Equations; Existence, Uniqueness and Equivalence of Solutions
The aim of this work is to prove existence and uniqueness of
solutions of stochastic fractional partial differential equations in
one spatial dimension. We prove also the equivalence between several notions of
solutions. The Fourier transform is used to give meaning to SFPDEs.
This method is valid also when the diffusion coefficient is random
Large deviations for 2D-fractional stochastic Navier-Stokes equation on the torus -Short Proof-
In this note, we prove the large deviation principle for the 2D-fractional
stochastic Navier-Stokes equation on the torus under the dissipation order .Comment: Work submitted to CRAS in 08-08-201
Ergodic properties of Fractional Stochastic Burgers Equation
We prove the existence and uniqueness of invariant measures for the
fractional stochastic Burgers equation (FSBE) driven by fractional power of the
Laplacian and space-time white noise. We show also that the transition measures
of the solution converge to the invariant measure in the norm of total
variation. To this end we show first two results which are of independent
interest: that the semigroup corresponding to the solution of the FSBE is
strong Feller and irreducible
Explicit solutions of some fractional partial differential equations via stable subordinators
The aim of this work is to represent the solutions of
one-dimensional fractional partial differential equations (FPDEs)
of order (α∈ℝ+\ℕ)
in
both quasi-probabilistic and probabilistic ways. The canonical
processes used are generalizations of stable Lévy processes.
The fundamental solutions of the fractional equations are given as
functionals of stable subordinators. The functions used generalize
the functions given by the Airy integral of Sirovich (1971). As a
consequence of this representation, an explicit form is given to
the density of the 3/2-stable law and to the density of escaping
island vicinity in vortex medium. Other connected FPDEs are also
considered
Ergodic properties of Fractional Stochastic Burgers Equation
We prove the existence and uniqueness of invariant measures for the fractional stochastic Burgers equation (FSBE) driven by fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariant measure in the norm of total variation. To this end we show first two results which are of independent
interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducibl
On a space discretization scheme for the Fractional Stochastic Heat Equations
In this work, we introduce a new discretization to the fractional Laplacian
and use it to elaborate an approximation scheme for fractional heat equations
perturbed by a multiplicative cylindrical white noise. In particular, we estimate the rate of convergenc