Limit Theory Of Markov Skeleton Processes And Its Applications

The concept of Markov skeleton process (MSP) was originated in 1997. This concept constitutes of a broad class of stochastic processes. In earlier study of MSP, the emphasis is laid on the transient behavior of these processes.In this doctoral thesis, first, an overview of transient behavior of MSP and the applications to queueing theory, reliability theory and inventory theory is presented. And with these results, I delve further into the theoretical issues of MSP and the concentration is on a special class of MSP-Doob skeleton processes. Generalized limit distribution, limit distribution of these processes and conditions and the expressions for the existence of invariable measure of such processes are provided. Finally, these new results are then applied to queueing theory, reliability theory and inventory theory.A detailed study of GI/G/1 queuing model, parallel connection system model, water reservoir model and perishable inventory model is discussed. These models have already been investigated to some degree. In particular, as mentioned above, some scholars have already successfully applied the transient behavior theory of MSP to these models and transient distributions of main variables in such models have been obtained. However, the limit behavior has not been addressed. In this thesis, limit behavior of main variables in the above-mentioned models is established.