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....
Taylor expansion of the density in a stochastic heat equation.
Temps d'explosion d'équations différentielles stochastiques du type Doléans-Dade
Temps locaux et intégration stochastique pour les processus de Dirichlet
The abstract Riemannian path space.
The approximate Euler method for Lévy driven stochastic differential equations
The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
The Banach fixed point method for Ito stochastic differential equations
The Banach space of workable contingent claims in arbitrage theory
The Bellman equation related to the minimal entropy martingale measure.
The central limit theorem for stochastic integrals.