Dubins-Freedman processes and RC filters
成果类型：
Article
署名作者：
Mazza, C; Piau, D
署名单位：
Universite Claude Bernard Lyon 1
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2001
页码：
1330-1352
关键词：
摘要：
We use McFadden's integral equations for random RC filters to study the average distribution of Dubins-Freedman processes. These distributions are also stationary probability measures of Markov chains on [0, 11, defined by the iteration of steps to the left x --> u x, and of steps to the right x - v + (1 - v) x, where u and v are random from [0, 1]. We establish new algorithms to compute the stationary measure of these chains. Turning to specific examples, we show that, if the distributions of u and I - v are Beta(a, 1), or Beta(a, 2), or if u and 1 - v are the exponential of Gamma(a, 2) distributed random variables, then the stationary measure is a combination of various hypergeometric functions, which are often F-3(2) functions. Our methods are based on a link that we establish between these Markov chains and some RC filters. We also determine the stationary distribution of RC filters in specific cases. These results generalize recent examples of Diaconis and Freedman.