This is a survey on the sample path properties of Markov processes, especially fractal properties of the random sets and measures determined by their sample paths. The class of Markov processes considered in this paper include Lévy processes in ℝ, diffusions on fractals and on ℝ, Feller...

An anticlique in N is a set of integers containing no pair of elements such that one is a multiple of the other. For every positive integer we give a necessary and sufficient condition on n for the set {1, 2, ..., } to admit an anticlique of cardinality containing

We use the recently-developed multiparameter theory of additive Lévy processes to establish novel connections between an arbitrary Lévy process in ℝ, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the...

Let = {(), ∈ ℝ} be an operator stable Lévy processes in ℝ with exponent , where is an invertible linear operator on ℝ. We determine the Hausdorff dimension and the packing dimension of the range ([0,1]) in terms of the real parts of the eigenvalues of

Long Term Fixed Income Market securities present a strong positive correlation in daily returns. By using a metrical approach and considering “modified” time series, I show how it is possible to show a more complex structure which depends strictly on the maturity date

This paper determines the vertices and surface volumes of all rounding polytopes for the most commonly used rounding methods: the quota method of greatest remainders and the divisor methods. These rounding methods are used to round continuous non-negative weights summing up to one to...

A continuous measure of the degree of mutual linear independence between the vectors of a given dataset, Continuous Significant Dimensionality (CSD), was introduced in the previous paper. In this report a simple and clear geometric interpretation of the CSD formula is determined, which has...

We provide a discussion of concave optimization theory subject to linear constraints and some robust applications of the theory including a study of homogeneous programming games and axiomatic analysis of the social choice rule which selects market equilibrium allocations

Some sharp inequalities of Grüss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coe cients in normed spaces are provided as well