My favorite topics of interest are the properties of Brownian motion, random walk and their local times. In the last few years I was working on the fine properties of iterated processes, logarithmic averages, some integral functional of certain stochastic processes. One of the main goal of my investigation was to develop a general strong approximation method which allow us to study certain processes through the investigation of the corresponding iterated process. This led to the strong approximation of a wide class of additive functionals.Another related topic of investigation was on the measure of heavily visited points of the Brownian motion.

Recently I got interested in the fine properties of the maximal local time and occupation time of the simple d-dimensional random walks. Questions about maximal local time on subsets, maximal occupation time of a finite set, multiplicity of the set of points with a given local time, and joint asymptotic behavior of local and occupation times of random walks in higher dimension are the object of my most recent work.