Editorial - Spring School Mons Random differential equations and gaussian fields
EDPS paraboliques à coefficients non—lipschitziens avec réflexion
Elliptic equations of higher stochastic order
This paper discusses analytical and numerical issues related to elliptic equations with random coefficients which are generally nonlinear functions of white noise. Singularity issues are avoided by using the Itô-Skorohod calculus to interpret the interactions between the coefficients and the solution. The solution is constructed by means of the Wiener Chaos (Cameron-Martin) expansions. The existence and uniqueness of the solutions are established under rather weak assumptions, the main of which...
Équation de Burgers avec conditions initiales à accroissements indépendants et homogènes
Équations aux dérivées partielles associées à un problème de filtrage non linéaire
Équations aux dérivées partielles stochastiques de type monotone
Équations aux dérivées partielles stochastiques : formulation faible
Equazioni stocastiche di un gas viscoso
Equivalence and Hölder-Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations
Ergodic behaviour of stochastic parabolic equations
The ergodic behaviour of homogeneous strong Feller irreducible Markov processes in Banach spaces is studied; in particular, existence and uniqueness of finite and -finite invariant measures are considered. The results obtained are applied to solutions of stochastic parabolic equations.
Ergodic control of linear stochastic equations in a Hilbert space with fractional Brownian motion
A linear-quadratic control problem with an infinite time horizon for some infinite dimensional controlled stochastic differential equations driven by a fractional Brownian motion is formulated and solved. The feedback form of the optimal control and the optimal cost are given explicitly. The optimal control is the sum of the well known linear feedback control for the associated infinite dimensional deterministic linear-quadratic control problem and a suitable prediction of the adjoint optimal system...
Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also...
Ergodicity for the stochastic complex Ginzburg–Landau equations
Ergodicity of stochastically forced large scale geophysical flows.
Essential m-dissipativity of Kolmogorov operators corresponding to periodic -Navier Stokes equations
We prove the essential m-dissipativity of the Kolmogorov operator associated with the stochastic Navier-Stokes flow with periodic boundary conditions in a space where is an invariant measure
Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations.
We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present papel is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial momentum. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations....
Étude probabiliste de l'opérateur de Schrödinger
Exact controllability for a nonlinear stochastic wave equation.
Existence and stability of solutions for nonautonomous stochastic functional evolution equations.
Existence and uniqueness of solutions for non-linear stochastic partial differential equations.
We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. In fact, we consider the equation dx(t) + (A(t,x(t)) + B(t,x(a(t))) + f(t)dt = (C(t,x(b(t)) + g(t))dwt, where A(t,·), B(t,·) and C(t,·) are suitable families of non linear operators in Hilbert spaces, wt is a Hilbert valued Wiener process, and a, b are functions of delay. If A satisfies a coercivity condition and a monotonicity hypothesis, and if B, C are Lipschitz continuous,...