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.