Limiting Behavior of Random Continued Fractions

作者：Lorentzen Lisa^*

来源：Constructive Approximation, 2013, 38(2): 171-191.

DOI：10.1007/s00365-013-9198-y

• Iterated function systems
• Random Mobius transformations
• Linear fractional transformations
• General convergence
• Restrained sequences
• Random composition sequences
• Random continued fractions
• Furstenberg%26apos
• s theorem

Let K(a (n) /b (n) ) be a continued fraction with elements (a (n) ,b (n) ) picked randomly and independently from according to some probability distribution mu. We find sufficient conditions on mu for K(a (n) /b (n) ) to converge with probability 1 or to be restrained with probability 1. More generally, we also consider mu-random sequences {tau (n) } of independent Mobius transformations and find sufficient conditions for to converge or be restrained with probability 1. The analysis is based on an important paper by Furstenberg.

• 出版日期2013-10