On the spectral analysis of second-order Markov chains
Annales de la faculté des sciences de Toulouse Mathématiques (2013)
- Volume: 22, Issue: 3, page 573-621
- ISSN: 0240-2963
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topDiaconis, Persi, and Miclo, Laurent. "On the spectral analysis of second-order Markov chains." Annales de la faculté des sciences de Toulouse Mathématiques 22.3 (2013): 573-621. <http://eudml.org/doc/275401>.
@article{Diaconis2013,
abstract = {Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm that the resort to second order Markov chains is an interesting option to improve the speed of convergence to equilibrium.},
author = {Diaconis, Persi, Miclo, Laurent},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {second-order Markov chains; spectral analysis; Markov kernel; trajectorial reversibility},
language = {eng},
month = {6},
number = {3},
pages = {573-621},
publisher = {Université Paul Sabatier, Toulouse},
title = {On the spectral analysis of second-order Markov chains},
url = {http://eudml.org/doc/275401},
volume = {22},
year = {2013},
}
TY - JOUR
AU - Diaconis, Persi
AU - Miclo, Laurent
TI - On the spectral analysis of second-order Markov chains
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 3
SP - 573
EP - 621
AB - Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding transition operators. Nevertheless and even if they are not diagonalizable in general, we study some features of their spectral decompositions and in particular the behavior of the spectral gap under appropriate perturbations is investigated. Our quantitative and qualitative results confirm that the resort to second order Markov chains is an interesting option to improve the speed of convergence to equilibrium.
LA - eng
KW - second-order Markov chains; spectral analysis; Markov kernel; trajectorial reversibility
UR - http://eudml.org/doc/275401
ER -
References
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