On extremal indices for some Markov chains induced by MCMC algorithms

• Autorzy: Wodecka B.
• Języki publikacji: EN

Abstrakty

EN

This paper gives examples of ergodic Markov chains produced by MCMC algorithms where the extremal index is zero.

Słowa kluczowe

EN

MCMC algorithms; stochastic processes; extremal indices; Markov chains

PL

algorytmy MCMC; procesy stochastyczne; ekstremalne wykładniki potęgi; łańuchy Markova

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 965--969
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Wodecka B.

• Mathematical Institute Świętokrzyska Academy ul. Świętokrzyska 15 25-406 Kielce, Poland

Bibliografia

• [1] P. Embrechts, C. Klüppelberg, T.Mikosch, Modelling Extremal Events, Springer, Berlin 1997.
• [2] A. Gut, Complete convergence and convergence rates for randomly indexed partial sums with an application to some first passage times, Acta Math. Hung. (1983), 225–235.
• [3] M. R. Leadbettter, G. Lindgren, H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York 1983.
• [4] M. R. Leadbettter, H. Rootzén, Extremal theory for stochastic processes, Annals of Probability 16 (1988), 431–478.
• [5] G. O. Roberts, J. S. Rosenthal, General state space Markov chains and MCMC algorithms, Probability Surveys, Vol. 1, 2004.
• [6] G. O. Roberts, J. S. Rosenthal, Markov chain Monte Carlo, preprint, Department of Mathematics and Statistics, Lancaster University, 2003
• [7] G. O. Roberts, J. S. Rosenthal, B. Sousa, Extremal Indices, Geometric Ergodicity of Markov Chains, and MCMC, preprint, Department of Mathematics and Statistics, Lancaster University, 2004.