A 2-dimensional SDE whose solutions are not unique.
A backward particle interpretation of Feynman-Kac formulae
We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We...
A characterisation of the closure of in
A characterization and moving average representation for stable harmonizable processes.
A characterization of harmonic sections and a Liouville theorem
Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .
A characterization of Markov solutions for stochastic differential equations with jumps
A characterization of random approximations.
A clark-ocone formula in UMD Banach spaces.
A comparison theorem for semimartingales and its applications
A comprehensive proof of localization for continuous Anderson models with singular random potentials
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand.
A conservative evolution of the Brownian excursion.
A converse comparison theorem for BSDEs and related properties of -expectation.
A converse to some inequalities and approximations in the theory of Stieltjes and stochastic integrals, and for nth derivatives
A counter-example concerning a condition of Ogawa integrability
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...
A coupled Cahn-Hilliard particle system.
A criterium for the strict positivity of the density of the law of a Poisson process.
A deterministic discretisation-step upper bound for state estimation via Clark transformations.
A dynamical system in a Hilbert space with a weakly attractive nonstationary point
A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty -set.