Random and deterministic perturbations of nonlinear oscillators.
Random fixed points and random differential inclusions.
Reflected backward stochastic differential equation with jumps and random obstacle.
Reflected backward stochastic differential equations with two RCLL barriers
In this paper we consider BSDEs with Lipschitz coefficient reflected on two discontinuous (RCLL) barriers. In this case, we prove first the existence and uniqueness of the solution, then we also prove the convergence of the solutions of the penalized equations to the solution of the RBSDE. Since the method used in the case of continuous barriers (see Cvitanic and Karatzas, Ann. Probab.24 (1996) 2024–2056 and Lepeltier and San Martín, J. Appl. Probab.41 (2004) 162–175) does not work, we develop...
Reflected diffusions defined via the extended Skorokhod map.
Réflexion discontinue et systèmes stochastiques
Règle maximale
Régularité des noyaux de Wiener d’une diffusion
Régularité de processus de sauts dégénérés
Regularity results for infinite dimensional diffusions. A Malliavin calculus approach
We prove some smoothing properties for the transition semigroup associated to a nonlinear stochastic equation in a Hilbert space. The proof introduces some tools from the Malliavin calculus and is based on a integration by parts formula.
Remarques sur l'intégrale stochastique
Representation of Itô integrals by Lebesgue/Bochner integrals
In [Yong 2004], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later...
Riccati equations and delay-dependent BIBO stabilization of stochastic systems with mixed delays and nonlinear perturbations.
Riesz transforms : a simpler analytic proof of P. A. Meyer's inequality
Robust estimates of certain large deviation probabilities for controlled semi-martingales
Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre...
Robust Filtering for Correlated Multidimensional Oberservations.
Robust option replication for a Black-Scholes model extended with nondeterministic trends.
Rolling with “slipping” : I