School Seminars and Colloquia

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