On weak convergence of sequences of continuous local martingales
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On weighted U-statistics for stationary random fields
The aim of this paper is to introduce a central limit theorem and an invariance principle for weighted U-statistics based on stationary random fields. Hsing and Wu (2004) in their paper introduced some asymptotic results for weighted U-statistics based on stationary processes. We show that it is possible also to extend their results for weighted -statistics based on stationary random fields.
One-dimensional finite range random walk in random medium and invariant measure equation
We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization...
One-dimensional random field Kac's model: weak large deviations principle.
Operator semigroups and Poisson convergence in selected metrics.
Operator theorems on -convergence to zero
Optimal bound for the discrepancies of lacunary sequences
The law of the iterated logarithm for discrepancies of lacunary sequences is studied. An optimal bound is given under a very mild Diophantine type condition.
Order Dentability and the Radon-Nikodym Property in Banach Lattices.
Ordered random walks.
Orthogonal polynomial ensembles in probability theory.
Oscillation presque sûre de martingales continues
Parabolic Harnack inequality and local limit theorem for percolation clusters.
Parry expansions of polynomial sequences.
Pathwise approximations of processes based on the fine structure of their filtrations
PDE-viscosity solution approach to some problems of large deviations
Penalisations of multidimensional Brownian motion, VI
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γt, we obtain here the existence of the limit, as t → ∞, of d-dimensional Wiener measures penalized by a function of the maximum up to time t of the Brownian winding process (for d = 2), or in {d}≥ 2 dimensions for Brownian motion prevented to exit a cone before time t. Various extensions of these multidimensional penalisations are studied, and the limit laws are described....
Penalization of the Wiener measure and principal values
Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process
Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when t → ∞. The main point of our work is that we do not suppose the process to be in...
Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process
Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when t → ∞. The main point of our work is that we do not suppose the process to be in...