Small ball probabilities for a class of time-changed self-similar processes

High resolution coding of stochastic processes and small ball probabilities

In this thesis, we study the high resolution coding problem for stochastic processes. The general coding problem concerns the finding of a good representation of a random signal, the original, within a class of allowed representations. The class of allowed representations is defined through restrictions on the information content of these representations. Mostly we consider three different inte...

Gaussian Processes: Inequalities, Small Ball Probabilities and Applications

Small Ball Probabilities for Gaussian Markov

A New Class of Second Order Self-Similar Processes

High Speed Networks Laboratory, Department of Telecommunications and Media Informatics Budapest University of Technology and Economics Magyar Tudósok körútja 2, H-1117 Budapest, Hungary ARC Special Research Center for Ultra-Broadband Information Networks Department of Electrical and Electronic Engineering The University of Melbourne, Australia. Alfréd Rényi Institute of Mathematics Hungarian Ac...

Small Time Expansions for Transition Probabilities of Some Lévy Processes

It has been proved that under additional assumptions, which in particular include the smoothness of Π, one gets more precise expansions of the probability P(X t ≥ y) and that these are polynomial in t. See [L, P, RW, FH2] among others. The problem of relating Π to the marginals of the process have several applications. The paper [RW], as well as [FH1], is concerned with problems of mathematical...