Sur l'unicité des solutions d'équations différentielles stochastiques
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE method...
Sur quelques algorithmes récursifs pour les probabilités numériques
The aim of this paper is to take an in-depth look at the long time behaviour of some continuous time Markovian dynamical systems and at its numerical analysis. We first propose a short overview of the main ergodicity properties of time continuous homogeneous Markov processes (stability, positive recurrence). The basic tool is a Lyapunov function. Then, we investigate if these properties still hold for the time discretization of these processes, either with constant or decreasing step (ODE...
Sur quelques approximations d'intégrales stochastiques
Sur quelques inégalités entre les moments absolus d'ordre positif d'une suite de variables aléatoires indépendantes et le second théorème — limite du calcul des probabilités au domaine de la loi de Laplace — Gauss dans la formulation de Liapounoff. II
Sur quelques inégalités entre les moments absolus d'ordre positif d'une suite de variables aléatoires indépendantes et le second théorème — limite du calcul des probabilités au domaine de la loi de Laplace — Gauss dans la formulation de Liapounoff. I
Sur une construction des solutions d'équations différentielles stochastiques dans le cas non-lipschitzien
Sur une équation d'évolution stochastique
Sur une équation différentielle stochastique générale
Sur une formule de la théorie du balayage
Sur une inégalité de Stein
SURE shrinkage of gaussian paths and signal identification
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
SURE shrinkage of Gaussian paths and signal identification*
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
We study points of density of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density is formulated in terms of the pointwise behaviour of the Ornstein-Uhlembeck semigroup.
Surface stretching for Ornstein Uhlenbeck velocity fields.
Symmetrized solutions for nonlinear stochastic differential equations.
Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods.
Synchronization of dissipative dynamical systems driven by non-Gaussian Lev́y noises.
Système de processus auto-stabilisants [Book]
Systemic risk through contagion in a core-periphery structured banking network
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets better than a symmetric model. The components of a vector Ornstein-Uhlenbeck process living on the nodes of the network describe the financial robustnesses of the agents. For this system, we prove a LLN for growing network size leading to a propagation of chaos result....