Math 564 : Applied Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions

Math 564 : Applied Stochastic Processes ( Fall 2017 ) Lecture : 18 Construction of CTMC

Stochastic Processes ( Fall 2017 ) Lecture : 10 Invariant Distributions

Suppose C is a closed recurrent communicating class for a Markov chain, if we restrict the chain on this class, the result is still a Markov chain with state space C. The resulting Markov chain is irreducible and recurrent. In this lecture, we will focus on the long-time behavior of irreducible and recurrent Markov chain. First, we have the following related definition. Definition 10.1. For a M...

Math 117 Lecture Notes

This is the set of lecture notes for Math 117 during Fall quarter of 2017 at UC Santa Barbara. The lectures follow closely the textbook [1].

Continuity of Generalized Semi-Markov Processes

It is shown that sequences of generalized semi-Markov processes converge in the sense of weak convergence of random functions if associated sequences of defining elements (initial distributions, transition functions and clock time distributions) converge. This continuity or stability is used to obtain information about invariant probability measures. It is shown that there exists an invariant p...

Heavy-Traffic Limits for the G/H2*/n/mQueue

We establish heavy-traffic stochastic-process limits for queue-length, waiting-time and overflow stochastic processes in a class of G/GI/n/m queueing models with n servers and m extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit theorem. To capture the impact of the service-time distribution beyond its mean within a Markovian f...