Averaging and stability of quasilinear functional differential equations with Markov parameters.
Backward doubly stochastic differential equations with infinite time horizon
We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.
Backward stochastic differential equations in a Lie group
Backward stochastic differential equations with oblique reflection and local Lipschitz drift.
Backward stochastic differential equations with stochastic monotone coefficients.
Backward stochastic differential equations with two distinct reflecting barriers and quadratic growth generator.
Behavior of the Euler scheme with decreasing step in a degenerate situation
The aim of this short note is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the diffusion coefficient are vanish simultaneously.
Bounded solutions of affine stochastic differential equations and stability
Boundedness and exponential stability of highly nonlinear stochastic differential equations.
Bounds for the range of American contingent claim prices in the jump-diffusion model
The problem of valuation of American contingent claims for a jump-diffusion market model is considered. Financial assets are described by stochastic differential equations driven by Gaussian and Poisson random measures. In such setting the money market is incomplete, thus contingent claim prices are not uniquely defined. For different equivalent martingale measures different arbitrage free prices can be derived. The problem is to find exact bounds for the set of all possible prices obtained in this...
Brownian dynamics of globules.
Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited
The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove that a limiting...
Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited
The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove...
Brownian penalisations related to excursion lengths, VII
Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.
BSDE associated with Lévy processes and application to PDIE.
BSDEs with polynomial growth generators.
BSDEs with two reflecting barriers driven by a Brownian and a Poisson noise and related Dynkin game.
Calcul de Malliavin pour les diffusions avec sauts : existence d'une densité dans le cas unidimensionnel
Calculs stochastiques directs sur les trajectoires et propriétés des boréliens porteurs
Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–Part I