Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 151-170

COVOLUTION POWERS OF PROBABILITES ON STOCHASTIC MATRICES OF ORDER 3

By

SANTANU CHAKRABORTY and B.V. RAO, Indian Statistical Institute, Calcutta

SUMMARY. In this note we show that for any probability on the space of $3 \times 3$ stochastic matrices, its convolution powers coverage unless some periodicities are present. This extends a result of A. Mukherjea for 2 x 2 case.

AMS (1991) subject classification. 15A52, 60B10, 60J15.

Key words and phrases. Stochastic matrices, semigroups, kernels, convolution, weak covergence.

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