Khanchi, Aziz2013-11-082013-11-0820082008Source: Dissertation Abstracts International, Volume: 70-02, Section: B, page: 1069.http://hdl.handle.net/10393/29543http://dx.doi.org/10.20381/ruor-13008We delve into a couple of topics in the theory of Markov chains and stochastic networks. The properties of a stable Markov chain X = (X1, Xˆ) will be investigated when X1 tends to infinity. We derive the distribution of Xˆ when X 1 passes a threshold for the first time as the threshold tends to infinity. Moreover, the exact asymptotics of the mean time until X 1 reaches the threshold is given. In addition, we present a new approach to determine the exact asymptotics of the X's steady state. The results are applied to an open modified Jackson network with two partially coupled processors. Finally, a ratio limit property is established for a Markovian kernel which has unbounded jumps.107 p.enMathematics.Thesis