Rare events & asymptotics for stationary distribution of Markov chains

Event Details
• Date/Time:
• Tuesday November 10, 2009 - Wednesday November 11, 2009
10:00 am - 10:59 am
• Location: IC 109
• Phone:
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• Fee(s):
\$0.00
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Contact
Anita Race
H. Milton Stewart School of Industrial and Systems Engineering
Contact Anita Race
Summaries

Summary Sentence: Rare events & asymptotics for stationary distribution of Markov chains

Full Summary: Rare events and asymptotics for the stationary distribution of Markov chains

TITLE: Rare events and asymptotics for the stationary distribution of Markov chains

SPEAKER: Dr. Robert Foley

ABSTRACT:

Markov processes are frequently used to model complex systems in a wide variety of areas including queueing and telecommunications. Often the Markov process has a stationary distribution \$pi\$ that cannot be explicitly determined. If \$pi(x)\$ is small, then state \$x\$ is rarely visited. Even though a state is visited infrequently, the state may represent an important event such as a failed system or an excessively large number of packets in a buffer in a telecommunications network. In well-designed systems, such events should be rare, but it can be critical to know how rare. Even attempting to estimate \$pi(x)\$ through simulation is fraught with difficulty when state \$x\$ is rarely visited. Consider a sequence of states \$x_ell\$ with \$pi(x_ell) to 0\$. Under certain conditions, we can derive exact asymptotic expressions for \$pi(x_ell)\$. That is, let \$x_ell\$ be a sequence of states with \$pi(x_ell) to 0\$. We can find \$a_ell\$ where \$pi(x_ell)/a_ell to 1\$. This approach can even handle situations in which the fluid limit of the large deviation path is not a straight line. We illustrate the approach on a queueing system.

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School of Industrial and Systems Engineering (ISYE)

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Categories
Seminar/Lecture/Colloquium
Keywords
Markov
Status
• Created By: Anita Race
• Workflow Status: Draft
• Created On: Feb 16, 2010 - 9:48am
• Last Updated: Oct 7, 2016 - 9:50pm