论文标题
关于在Homeo（R）的随机步行的不变措施的独特性（R）
On uniqueness of invariant measures for random walks on HOMEO(R)
论文作者
论文摘要
我们考虑在实际行$ {\ mathbb r} $的方向保护同态同态上随机步行。特别是，提出了对生成过程不变衡量的独特性的基本问题。 Choquet and Deny（1960）已经研究了该问题的情况下，该问题是在线条翻译产生的随机步行中。如今，在强有力的系统的一般环境中，答案已被充分理解。在这里，我们专注于满足条件的更广泛的系统：复发，收缩和无限的作用。我们证明，在这种情况下，随机过程在$ {\ mathbb r} $上具有独特的不变ra。我们的工作可以看作是Babillot等人的随后论文。 （1997）和Deroin等。 （2013）。
We consider random walks on the group of orientation-preserving homeomorphisms of the real line ${\mathbb R}$. In particular, the fundamental question of uniqueness of an invariant measure of the generated process is raised. This problem was already studied by Choquet and Deny (1960) in the context of random walks generated by translations of the line. Nowadays the answer is quite well understood in general settings of strongly contractive systems. Here we focus on broader class of systems satisfying the conditions: recurrence, contraction and unbounded action. We prove that under these conditions the random process possesses a unique invariant Radon measure on ${\mathbb R}$. Our work can be viewed as a subsequent paper of Babillot et al. (1997) and Deroin et al. (2013).
