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We consider a process Z on the real line composed from a Levy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of the supremum (Z) over bar, its time T, and the process Z(T + center dot) - (Z ...
We establish in the world of stochastic processes a theoretical relation between sparsity and wavelets. The underlying principle is to treat stochastic processes as generalized functions, which facilitates the study of their properties in a transform domai ...
In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise. More precisely, we describe new sample paths properties of a given noise in terms of weighted Besov spaces. In particular, we characterize the smoothness and integrab ...
In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...
Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...
We provide a detailed study of the interplay between the different interactions which appear in the Brownian motion of a micronsized sphere immersed in a viscoelastic fluid measured with optical trapping interferometry. To explore a wide range of viscous, ...
We study the interface of the symmetric multitype contact process on Z. In this process, each site of Z is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give birth with rate 2R lambda; the ...
We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...
Schizophrenia impairs cognitive function as much as perception. For example, patients perceive global motion in random dot kinematograms less strongly, because the integration of the dots into a single Gestalt is complex (e.g., Chen, Nakayama, Levy, Matthy ...
A constrained informationally efficient market is defined as one in which the price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which, desp ...