Identifications optimales de paramètres pour un système linéaire excité par un bruit gaussien
Images d'équations différentielles stochastiques
Inéquations quasi variationnelles dépendant d'un paramètre
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
Integration by parts for jump processes
Introduction to the Theory of the It-type Stochastic Integrals and Stochastic Differential Equations
Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations
We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.
Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup.
Invariant measures related with randomly connected Poisson driven differential equations
We consider the stochastic differential equation (1) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup describing the evolution of measures along trajectories and vice versa.
Itô's formula with respect to fractional Brownian motion and its application.