Related papers: On universality in penalisation problems with mult…
In this monograph, we construct and study a sigma-finite measure on continuous functions from R_+ to R, strongly related to many probability measures obtained by penalisation of Brownian motion, i.e. as limits of probabilities which are…
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable L\'evy process of index $ 1 < \alpha \le 2 $. The first kind is a function of the local time at the origin, and the…
In this paper, we give a global view of the results we have obtained in relation with a remarkable class of submartingales, called $(\Sigma)$, and its links with a universal sigma-finite measure and penalization problems on the space of…
In a previous work, we associated with any submartingale $X$ of class $(\Sigma)$, defined on a filtered probability space $(\Omega, \mathcal{F}, \mathbb{P}, (\mathcal{F}_t)_{t \geq 0})$ satisfying some technical conditions, a…
In this paper, we construct a family of probability measures, by penalizations of a Walsh Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t…
We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional L\'{e}vy processes. The limit processes may vary according to the choice of random…
We establish global universal approximation theorems on spaces of piecewise linear paths, stating that linear functionals of the corresponding signatures are dense with respect to $L^p$- and weighted norms, under an integrability condition…
In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as…
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…
We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1,1]. Assume that mu is a regular measure, and is absolutely continuous in an open…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
In our monograph with B. Roynette and M. Yor, we construct a sigma-finite measure related to penalisations of different stochastic processes, including the Brownian motion in dimension 1 or 2, and a large class of linear diffusions. In the…
In this article, we study the family of probability measures (indexed by a positive real number t), obtained by penalization of the Brownian motion by a given functional of its local times at time t. We prove that this family tends to a…
We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be…
We present a so-called universal convergence theorem for inexact primal-dual penalty and augmented Lagrangian methods that can be applied to a large number of such methods and reduces their convergence analysis to verification of some…
Several long-time limit theorems of one-dimensional L\'evy processes weighted and normalized by functions of its supremum are studied. The long-time limits are taken via the families of exponential times and that of constant times, called…
We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this multiplicative functional, converges as t…
It is shown that many of the classical generalized isoperimetric inequalities for the Laplacian when viewed in terms of Brownian motion extend to a wide class of Levy processes. The results are derived from the multiple integral…
In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally…
This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…