Probability theory has long provided a rigorous framework for quantifying uncertainty, yet its extension to infinite sets introduces profound conceptual challenges and opportunities. Contemporary ...

PROBABILITY theory is a quaint little piece of mathematics. It is about sets of non-negative numbers that are attached to actual and possible physical events, that sum to 1 and that obey certain rules ...

It is shown that a class of infinite, block-partitioned, stochastic matrices has a matrix-geometric invariant probability vector of the form (x0,x1,...), where xk=x0Rk, for k≥ 0. The rate matrix R is ...