Algorithmic Analysis of Stochastic Models

The progress in computing and communications technologies made in the last quarter of the past Century has not only ushered in the \Information Age," but it has also in uenced the basic sciences, including mathematics, in fundamental ways. Thanks to the signi cantly increased computing power, mathematicians can now augment classical techniques of analysis, proof and solution with an algorithmic approach in a manner that enables the consideration of more complex models with wider applicability, and also obtain results with greater practical value to engineering. While providing powerful tools to the mathematician, the technologies, nevertheless, are also posing new challenges and problems, and opening many new vistas for further mathematical research. Among the areas exemplifying all these, a notable one is algorithmic methods for stochastic models based on \the matrix (operator) analytic method." This lecture is an overview of those methods.