Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Dan Shen, Ph.D.

Committee Member

Lu Lu, Ph.D.


Cyber Security, Markov Model, Vulnerability, Risk Factor, Vulnerability Life Cycle


Analysis on Vulnerabilities and Vulnerability Life Cycle is at the core of Cybersecurity related studies. Vulnerability Life Cycle discussed by S. Frei and studies by several other scholars have noted the importance of this approach. Application of Statistical Methodologies in Cybersecurity related studies call for a greater deal of new information. Using currently available data from National Vulnerability Database this study develops and presents a set of useful Statistical tools to be applied in Cybersecurity related decision making processes.

In the present study, the concept of Vulnerability Space is defined as a probability space. Relevant theoretical analyses are conducted and observations in the vulnerability space in aspects of events and states are discussed.

Transforming IT related cybersecurity issues into analytical formation so that abstract and conceptual knowledge from Mathematics and Statistics can be applied is a challenge. However, to overcome rising threats from Cyber-attacks such an integration of analytical foundation to understand the issues and develop strategies is essential. In the present study we apply well known Markov approach in a new approach of Vulnerability Life Cycle to develop useful analytical methods to assess the Risk associated with a vulnerability. We also presents, a new Risk Index integrating the results obtained and details from the Common Vulnerability Scoring System (CVSS).

In addition, a comprehensive study on the Vulnerability Space is presented discussing the likelihood of probable events in the probability sub-spaces of vulnerabilities.

Finally, an Extended Vulnerability Life Cycle model is presented and discussed in relation to States and Events in the Vulnerability Space that lays down a strong foundation for any future vulnerability related analytical research efforts.