Stochastic Models

This course includes stochastic processes that are popular in scientific applications, such as discrete time Markov chains, the Poisson process, continuous time Markov processes, long run behavior of Markov chains and Birth and Death Processes. Stochastic processes are ways of quantifying the dynamic relationships of sequences of random events. Stochastic models play an important role in elucidating many areas of the natural and engineering sciences. They can be used to analyze the variability inherent in biological and medical processes, to deal with uncertainties affecting managerial decisions and with the complexities of psychological and social interactions, and to provide new perspectives, methodology, models, and intuition to aid in other mathematical and statistical studies.

Upon the successful completion of this course, students should be able to:

• apply the concepts and investigation results of the long-run behavior of simple stochastic processes in discrete time Markov chains.
• apply the standard concepts and methods of stochastic modeling to the Information Technology fields of studies.
• illustrate the rich diversity of applications of stochastic processes in the sciences.
• evaluate problems in the application of stochastic modeling.
• apply stochastic modeling to the appropriate problems in Software Engineering, Business Information System, Knowledge Engineering, Communication Networking, Embedded System and High Performance Computing.

Textbooks:

1. An Introduction To Stochastic Modeling, Howard M. Taylor Samuel Karlin

References:

1. Markov Processes for Stochastic Modeling, Oliver C.Ibe, University of Massachusetts Lowell
2. A First Course in Stochastic Models, Henk C.Tijms