Thermodynamic formalism for random countable Markov shifts
Thermodynamic formalism for random countable Markov shifts
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DOI：
10.3934/dcds.2008.22.131
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发表时间：
2008-06
影响因子：
1.1
通讯作者：
M. Denker;Y. Kifer;M. Stadlbauer
中科院分区：
文献类型：
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作者：
M. Denker;Y. Kifer;M. Stadlbauer
本文对随机可数拓扑混合马氏位移引入了一个相对Gurevich压力。它表明，相对变分原理适用于这种压力的概念。我们还证明了一个相对的Ruelle-Perron-Frobenius定理，使我们能够构建一个丰富的不变的吉布斯措施，局部纤维保持器连续的功能。这是通过一个新的建设一个等变家庭的纤维措施，使用克劳埃尔的相对Prohorov定理。讨论了Gibbs测度的一些性质。
We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the relative variational principle holds for this notion of pressure. We also prove a relative Ruelle-Perron-Frobenius theorem which enables us to construct a wealth of invariant Gibbs measures for locally fiber Holder continuous functions. This is accomplished via a new construction of an equivariant family of fiber measures using Crauel's relative Prohorov theorem. Some properties of the Gibbs measures are discussed as well.