On a class of perimeter-type distances of probability distributions
We consider processes Xₜ with values in and “time” index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand’s majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.
The busy period distribution of a discrete modified queue , with finitely or infinitely many severs , and with different distribution functions of customer service times is derived.