Probability measures on 2 × 2 stochastic matrices: some open problems

✍ Scribed by A. Mukherjea; J.S. Ratti

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 255 KB
• Volume: 30
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(96)00271-4

✦ Synopsis

Let p be a probability measure on 2 x 2 stochastic matrices with finite support such that the sequence pn 3 the nth convolution power of p, weakly converges to a probability measure X whose support consists of 2 x 2 stochastic matrices with identical rows. The probability measure A can, therefore, be regarded as a measure on the unit interval [0, I]. In this paper, we discuss some open problems regarding when X is continuous singular or absolutely continuous with respect to the Lebesgue measure on [0, 11, and when X determines ~1 uniquely.