On the stability of stationary solutions of a linear integro-differential equation.
On the stabilization of the energy of a harmonic oscillator disturbed by random processes of the “white and shot noises” types.
On the stochastic regularity of sequence transformations operating in a Banach space
On the strong convergence to equilibrium for randomly perturbed dynamical systems
On the unique solvability of some nonlinear stochastic PDEs.
On the uniqueness of solutions of stochastic differential equations with reflecting barrier conditions
On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
In [Probab. Theory Related Fields141 (2008) 543–567], the authors proved the uniqueness among the solutions of quadratic BSDEs with convex generators and unbounded terminal conditions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman–Kac formula proved...
On the variance of the number of real roots of a random trigonometric polynomial.
On transformations of Wiener space.
On two transfer principles in stochastic differential geometry
On uniform exponential -dichotomy
On uniqueness of a solution of with given trace.
On variant reflected backward SDEs, with applications.
Onsager-Machlup functional for stochastic evolution equations
Onsager-Machlup functionals for solutions of stochastic boundary-value problems
Opérateurs d'échange et quelques applications des méthodes de noyaux
Opérateurs filtrés et chaînes de tribus invariantes sur un espace probabilisé dénombrable
Optimal contracts in continuous-time models.
Optimal control of a stochastic heat equation with boundary-noise and boundary-control
We are concerned with the optimal control of a nonlinear stochastic heat equation on a bounded real interval with Neumann boundary conditions. The specificity here is that both the control and the noise act on the boundary. We start by reformulating the state equation as an infinite dimensional stochastic evolution equation. The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The C1 regularity...
Optimal position targeting with stochastic linear-quadratic costs
We consider the dynamic control problem of attaining a target position at a finite time T, while minimizing a linear-quadratic cost functional depending on the position and speed. We assume that the coefficients of the linear-quadratic cost functional are stochastic processes adapted to a Brownian filtration. We provide a probabilistic solution in terms of two coupled backward stochastic differential equations possessing a singularity at the terminal time T. We verify optimality of the candidate...