For n [greater-or-equal, slanted] 2 an (n - 1)-parameter real process Vn, called stochastic volume, is defined. This process is an extension to higher dimensions of Lévy's stochastic area which is obtained from Vn by setting n = 2. For V3, a Strassen-type functional law of the iterated...

It is shown that unimodality (discrete or not) is preserved by mixing for certain distributions. The technique of proof is essentially based on the Representation Theorem of Khinchin which characterizes unimodality.

Let F be a discrete distribution function on . This paper gives a characterization of discrete unimodal distribution functions (Theorem 5.1) and a representation theorem for those distribution functions (Theorem 6.3), both in terms of their Lévy concentration functions.

The aim of this paper is to examine multiple Markov dependence for the discrete as well as for the continuous parameter case. In both cases the Markov property with arbitrary parameter values is investigated and it is shown that it leads to the degeneration of the multiple Markov dependence to...

Three types of unimodality (central convex, block, and star) are considered and the corresponding sets of unimodal copulas determined. Examples of star unimodal copulas, absolutely continuous, with a nonnull singular part, and even singular, are given. Necessary and sufficient conditions for a...

In applications it often occurs that the experimenter is faced with functions of random processes. Suppose, for instance, that he only can draw partial or incomplete information about the underlying process or that he has to classify events for the sake of efficiency. We assume that the...