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

To many, the concept of probability feels intuitive. We're used to thinking about the odds of everything from coin flips to election results. Probability has become so integral to everyday life, it's ...

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 ...