Omar Khalil - Queen's University

More documents

Recommendations

Info

useful techniques for analysing stochastic stability of Markov chains in general. The state dependent random sampling criteria proves to have many practical applications. Natural steps beyond this paper include generalizing theorems 1 and 2 to results where both these theorems are special cases and which do not necessarily include the geometric growth condition. Fur- thermore one may want to consider analysing the rates of convergence of the Markov chains which is of particular importance in real time control systems. 10
5 References [1] Meyn, S.P. and Tweedie, R. (1994) State-dependent criteria for convergence of Markov chains Ann. Appl. Probab. 4 149-168. [2] Meyn, S. P. and Guo, L. (1992). Stability, convergence, and performance of an adaptive control algorithm applied to a randomly varying system. IEEE Trans. Automat. Control AC-37 535-540. [3] Chen, R and Tsay, R.S. (1991). On the ergodicity of TAR(1) processes. Ann. Appl. Probab. 1 613-634. [4] Tjøsthem, D. (1990). Non–linear time series and Markov chains. Adv. in Appl. Probab. 22 587-611. [5] Malyˇshev, V. A. and Men’ˇsikov, M. V. (1982). Ergodicity, continuity and analyticity of countable Markov chains. Trans. Moscow Math. Soc. 1 1-48. [6] Yüksel, S. (2009). A Random Time Stochastic Drift Result and Application to Stochastic Stabilization Over Noisy Channels. Allerton Conference, Illinois, USA. [7] Yüksel, S. and Meyn. S. P. (2010). Random-Time, State-Dependent Stochastic Drift for Markov Chains and Application to Stochastic Stabilization Over Erasure Channels. IEEE Trans. Automat. Control. [8] Yüksel, Serdar. (2011). Math 472/872 Course Lecture Notes. Queen’s <strong>University</strong>. [9] It ô, Kiyosi. Introduction to Probability Theory. Cambridge <strong>University</strong> Press, 1986. 11
Page 1 and 2: State-Dependent Criteria for Conver
Page 3 and 4: 1 Introduction The problem of estab
Page 5 and 6: for all x ∈ X and n ∈ Z+. We me
Page 7 and 8: We will also define for non-negativ
Page 9: not necessarily geometric in nature

Omar Khalil - Queen's University

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?