# Stationary solutions of some random recurrences/Occupation times for continuous time Markov chains

*by Talks by Honours/PGDip Students*

*Institution:*Mathematics and Statistics Dept, The University of Melbourne

*Date: Thu 22nd October 2009*

*Time: 3:15 PM*

*Location: Old Geology Theatre 2, The University of Melbourne*

*Abstract*: Speaker 1: Yunshun Chen

Title:

Stationary solutions of some random recurrences.

Abstract: The questions of existence and uniqueness of solutions to random

equations first arose in queueing theory. One typical example is the

famous Lindley equation, W=max(0,W+X). In the 1980s, this kind of random

recurrence was also studied in detail by C. Goldie, basing on implicit

renewal theory. In this talk, we will have a brief look at some types of

random equations and results obtained by Goldie. The existence and

uniqueness of the solution, as well as the solution's distribution tail

behaviour for certain random equations, will also be discussed.

Speaker 2: Shaun McKinlay

Title: Occupation times for continuous time Markov chains

Abstract: This talk is on the distribution of the occupation times of for

continuous time Markov chains. Occupation times refer to the total time

spent in a single state of a continuous time Markov chain, in a finite

time interval. We first derive the Laplace transform for the occupation

time, then use this to derive the occupation time distribution in a two

state Markov chain. [Mostly based on papers by Pedler (1971) and Darroch

and Morris (1967).]

*For More Information:* contact: Aihua Xia. email: aihuaxia@unimelb.edu.au