On explicit form of the stationary distributions for a class of bounded Markov chains

摘要: We consider a class of discrete time Markov chains with state space [0, 1] and the following dynamics. At each step, first direction next transition is chosen at random probability depending on current location. Then length jump independently as proportion distance to respective end point unit interval, distributions proportions being fixed for two directions. Chains that kind were subjects number studies are interest some applications. Under simple broad conditions, we establish ergodicity such then derive closed form expressions stationary densities when beta distributed parameter equal 1. Examples demonstrating range processes described by this model given, an application robot coverage algorithm discussed.