A weak quasi-Lindelöf property and quasi-fine supports of measures.
Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height . In the quenched setting, we also sharply estimate the distribution of the walk at time .
An asymptotic expansion for the discrete harmonic potential.
An extended generator and Schrödinger equations.
An extension of a boundedness result for singular integral operators
We study some operators originating from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one-dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are the G* and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on . Moreover, we generalize a classical multiplier theorem by weakening its...
Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
Anomalous heat-kernel decay for random walk among bounded random conductances
We consider the nearest-neighbor simple random walk on ℤd, d≥2, driven by a field of bounded random conductances ωxy∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of ωxy>0 exceeds the threshold for bond percolation on ℤd. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2n-step return probability . We prove that is bounded by a random constant timesn−d/2 in d=2, 3, while it...
Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space
Appendice à : « Intégral de capacités fortement sous-additives »
Application d'un théorème de Mokobodzki aux opérateurs potentiels dans le cas récurrent
Approximation of arbitrary Dirichlet processes by Markov chains
Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes.
Avoiding-probabilities for Brownian snakes and super-Browian motion.
Balayage de fonctions excessives
Bernstein Theorems for Harmonic Morphisms from R3 and S3.
Bivariate Revuz measures and the Feynman-Kac formula
Boundary potential theory for stable Lévy processes
We investigate properties of harmonic functions of the symmetric stable Lévy process on without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for...
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Brownian motion on fractals and function spaces.