Dissertation Defence: Confidence Intervals and Regions for Steady-State Probabilities and Additive Functionals based on a Single Sample Path of a Markov Chain
February 28 at 9:00 am - 1:00 pm
Yann Vestring, supervised by Dr. Javad Tavakoli, will defend their dissertation titled “Confidence Intervals and Regions for Steady-State Probabilities and Additive Functionals based on a Single Sample Path of a Markov Chain” in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics.
An abstract for Yann Vestring’s dissertation is included below.
Examinations are open to all members of the campus community as well as the general public. Please email javad.tavakoli@ubc.ca to receive the Zoom link for this exam.
ABSTRACT
When a system is modelled as a Markov chain, the asymptotic properties of the system, such as the steady-state distribution, are often estimated based on a single, empirically observable sample path of the system, whereas the actual steady-state distribution is unknown. A question that arises is: how close is the empirically estimated steady-state distribution to the actual steady-state distribution? In this thesis, we explore how we might numerically determine confidence regions for the steady-state probabilities and confidence intervals for additive functionals of an ergodic Markov chain based on a single sample path.
