Identification of stochastic loads applied to a nonlinear dynamical system using an uncertain computational model.
Identifications optimales de paramètres pour un système linéaire excité par un bruit gaussien
Images d'équations différentielles stochastiques
Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients⋆⋆⋆
In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product. We consider then the Stochastic Collocation method, and use the previous estimates to introduce...
Incompleteness of the bond market with Lévy noise under the physical measure
The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.
Indefinite quadratic functionals of gaussian processes and least-action paths
Inégalités de normes pour les intégrales stochastiques
Inégalités de Sobolev faibles : un critère
Inégalités isopérimétriques et calcul stochastique
Inéquations quasi variationnelles dépendant d'un paramètre
Infinite dimensional Gegenbauer functionals
he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
Infinite products of random matrices and repeated interaction dynamics
Let Ψn be a product of n independent, identically distributed random matrices M, with the properties that Ψn is bounded in n, and that M has a deterministic (constant) invariant vector. Assume that the probability of M having only the simple eigenvalue 1 on the unit circle does not vanish. We show that Ψn is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as n→∞. The fluctuating part converges in Cesaro mean to a limit that is characterized...
Infinite system of Brownian balls with interaction: the non-reversible case
We consider an infinite system of hard balls in undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.
Infinitesimal behaviour of a continuous local martingale
Initial data stability and admissibility of spaces for Itô linear difference equations
The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the -stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive...
Initial measures for the stochastic heat equation
We consider a family of nonlinear stochastic heat equations of the form , where denotes space–time white noise, the generator of a symmetric Lévy process on , and is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that for some , we prove that if is a finite measure of compact support, then the solution is...
Integral inequality and exponential stability for neutral stochastic partial differential equations with delays.
Integral representation of martingales in the brownian excursion filtration
Intégrale multiple de Stratonovich pour le processus de Poisson
Intégrale stochastique curviligne le long d'une courbe rectifiable