On the unboundedness of martingale transforms
On Walsh's brownian motions
On weak convergence of sequences of continuous local martingales
Optimal linear filtering of general multidimensional Gaussian processes and its application to Laplace transforms of quadratic functionals.
Optimal solutions to stochastic differential inclusions
A martingale problem approach is used first to analyze compactness and continuous dependence of the solution set to stochastic differential inclusions of Ito type with convex integrands on the initial distributions. Next the problem of existence of optimal weak solutions to such inclusions and their dependence on the initial distributions is investigated.
Optional splitting formula in a progressively enlarged filtration
Let F be a filtration andτbe a random time. Let G be the progressive enlargement of F withτ. We study the following formula, called the optional splitting formula: For any G-optional processY, there exists an F-optional processY′ and a function Y′′ defined on [0,∞] × (ℝ+ × Ω) being ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random timesτ1,...,τk). We are interested in this formula because of its fundamental role in many...
Orlicz space - valued martingales
Orthogonalité et uniforme intégrabilité de martingales. Étude d'une classe d'exemples
Oscillation presque sûre de martingales continues