论文标题
马尔可夫运营商在抽象状态空间上的均匀$ p $ ergodicities的光谱条件
Spectral conditions for uniform $P$-ergodicities of Markov operators on abstract states spaces
论文作者
论文摘要
在本文中，涉及作用于抽象状态空间的马尔可夫操作员的渐近稳定性（即，在正常元素上具有添加性特性的有序Banach空间）。基本上，当Markov运营商$ t $满足统一$ p $ - 果态，即$ \ | t^n-p \ | \ 0 $时，我们对收敛速度感兴趣。我们已经表明，$ t $在且仅当$ \ | t^n-p \ | \ leqcβ^n $，$ 0 <β<1 $时，$ t $均匀地$ p $ ergodic。在本文中，我们证明了这样的$β$的特征是光谱半径为$ t-p $。此外，我们为马尔可夫运营商的统一$ p $ erergodity提供了Deoblin的条件。
In the present paper deals with asymptotical stability of Markov operators acting on abstract state spaces (i.e. an ordered Banach space, where the norm has an additivity property on the cone of positive elements). Basically, we are interested in the rate of convergence when a Markov operator $T$ satisfies the uniform $P$-ergodicity, i.e. $\|T^n-P\|\to 0$, here $P$ is a projection. We have showed that $T$ is uniformly $P$-ergodic if and only if $\|T^n-P\|\leq Cβ^n$, $0<β<1$. In this paper, we prove that such a $β$ is characterized by the spectral radius of $T-P$. Moreover, we give Deoblin's kind of conditions for the uniform $P$-ergodicity of Markov operators.
