Markov Processes & Spectral Theory

Themes in recent research are application of Markov chain and large deviation theory methods to Monte-Carlo based algorithms for estimation and control.

Research on spectral theory is pursued in part for its intrinsic beauty, and in part because of its wide-spread potential application to many fields. For example, these methods are favored in the DyNARUM project, and research at United Technologies Research Center

Meyn, S.P. and R. Tweedie, Markov Chains & Stochastic Stability, Springer-Verlag, N.Y. New edition to appear, Cambridge University Press, 2008.

I. Kontoyiannis, L.A. Lastras-Montaño, and S.P. Meyn, Relative Entropy and Exponential Deviation Bounds for General Markov Chains, ISIT 2005.

J. Huang, Kontoyiannis, I. and S.P. Meyn, The O.D.E. Method and Spectral Theory of Markov Operators (also available in pdf format), Proceedings of the Second Kansas Workshop on Stochastic Theory - Adaptive Control, 2001.

Kontoyiannis, I. and S.P. Meyn, Spectral Theory and Limit Theory for Geometrically Ergodic Markov Processes, Annals of Applied Prob., Volume 13, pp. 304-362, 2003.

Kontoyiannis, I. and S.P. Meyn, Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes, Electronic Journal of Probability, vol. 10, no. 3, pp. 61-123, 2005. (electronic)

W. Huisinga, S. P. Meyn, and C. Schuette. Phase Transitions & Metastability in Markovian and Molecular Systems

C. Schuette, W. Huisinga, S. P. Meyn. Metastability of Diffusion Processes Proceeding of the IUTAM Symposium on Nonlinear Stochastic Dynamics (August 26 - August 30, 2002, Illinois/USA), 2003.

Balaji, S. and S.P. Meyn, Multiplicative Ergodicity and Large Deviations for an Irreducible Markov Chain, Stochastic Processes and Their Application, Vol. 1, 2000, pp. 123-144. (also available in pdf format)

Down, D., S.P. Meyn and R. Tweedie Exponential and Uniform Ergodicity of Markov Processes, Annals of Probability, 23:1671-1691, 1996.

Meyn, S.P. and R. Tweedie, A Survey of Foster-Lyapunov Conditions for General State Space Markov Processes, in Proceedings of the Workshop on Stochastic Stability and Stochastic Stabilization, Metz, France, June 1993, Springer-Verlag, 1994.

Glynn, P. and S. Meyn A Lyapunov Bound for Solutions of Poisson's Equation, Annals of Probability, Vol. 24, April, 1996.

Meyn, S.P. and R.L. Tweedie, Generalized Resolvents and Harris Recurrence of Markov Processes, (also available in pdf format). Collected papers from the workshop 50 years after Doeblin: Developments in the theory of Markov chains, Markov processes and sums of random variables. Published in Doeblin and Modern Probability, Contemporary Mathematics, Providence, RI, Proceedings of the Doeblin Conference held November 2-7, 1991 at the University of Tubingen's Heinrich Fabri Institut, pp. 227--249, 1993.

Meyn, S.P. and R.L. Tweedie, The Doeblin Decomposition, collected papers from the workshop 50 years after Doeblin: Developments in the theory of Markov chains, Markov processes and sums of random variables. Published in Doeblin and Modern Probability, Contemporary Mathematics, Providence, RI, Proceedings of the Doeblin Conference held November 2-7, 1991 at the University of Tubingen's Heinrich Fabri Institut, pp. 211--225, 1993.

Meyn, S.P. and R.L. Tweedie, Computable Bounds For Convergence Rates of Markov Chains, Annals of Applied Probability, Vol. 4, September, 1994.

Meyn, S.P. and R.L. Tweedie, Criteria for stability of Markovian processes III: Foster-Lyapunov criteria for continuous time processes, with examples, Advances in Applied Probability, Vol. 25, pp. 518--548, 1993.