The stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation ...

If an n x n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper ...

Random walks serve as fundamental models in the study of stochastic processes, simulating phenomena ranging from molecular diffusion to queuing networks and financial systems. Their inherent ...

The magic of mathematics is particularly reflected in magic squares. Recently, quantum physicists and mathematicians introduced the notion of the quantum magic square, and for the first time studied ...