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Rates of convergence for products of random stochastic 2 × 2 matrices

Part of: Geometric probability and stochastic geometry Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Ralph Neininger
Ralph Neininger*
Affiliation:
Albert-Ludwigs-Universität Freiburg
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Abstract

Products of independent identically distributed random stochastic 2 × 2 matrices are known to converge in distribution under a trivial condition. Rates for this convergence are estimated in terms of the minimal Lp-metrics and the Kolmogoroff metric and applications to convergence rates of related interval splitting procedures are discussed.

Keywords

Random stochastic matrixrate of convergenceKolmogoroff metricrandom walkinterval splitting

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60D05: Geometric probability and stochastic geometry 60E05: Distributions
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 799 - 806
Copyright
Copyright © by the Applied Probability Trust 2001 

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References

Bickel, P. J., and Freedman, P. A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9, 1196–1217.CrossRefGoogle Scholar
Chen, R., Goodman, R., and Zame, A. (1984). Limiting distributions of two random sequences. J. Multivar. Anal. 14, 221–230.Google Scholar
Chen, R., Lin, E., and Zame, A. (1981). Another arc sine law. Sankhyā A 43, 371–373.Google Scholar
Devroye, L., Letac, G., and Seshadri, V. (1986). The limit behavior of an interval splitting scheme. Statist. Prob. Lett. 4, 183–186.CrossRefGoogle Scholar
Herz, C. (1988). Splitting intervals. Statist. Prob. Lett. 7, 3–7.Google Scholar
Kennedy, D. P. (1988). A note on stochastic search methods for global optimization. Adv. Appl. Prob. 20, 476–478.Google Scholar
Letac, G., and Scarsini, M. (1998). Random nested tetrahedra. Adv. Appl. Prob. 30, 619–627.Google Scholar
Rosenblatt, M. (1964). Equicontinuous Markov operators. Teor. Verojat. Primen. 9, 205–222.Google Scholar
Sun, T.-C. (1975). Limits of convolutions of probability measures on the set of 2*2 stochastic matrices. Bull. Inst. Math. Acad. Sinica 3, 235–248.Google Scholar
Van Assche, W. (1986). Products of 2*2 stochastic matrices with random entries. J. Appl. Prob. 23, 1019–1024.Google Scholar
Vervaat, W. (1979). On a stochastic difference equation and a representation of non-negative infinitely divisible random variables. Adv. Appl. Prob. 11, 750–783.Google Scholar