Markov Extensions and Conditionally Invariant Measures for Certain Logistic Maps with Small Holes

关于具有无界转移密度的吸收马尔可夫链的准遍历性，包括带逃逸的随机逻辑斯蒂映射

On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape

本文研究具有无界转移密度的吸收马尔可夫链的准遍历性，给出准遍历测度存在及Yaglom极限收敛的条件，并将其应用于带逃逸的随机逻辑斯蒂映射。

On Transfer Operators and Maps with Random Holes

We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise, we show that the transfer operator associated with the random open system can be reduced to a transfer operator associated with the closed deterministic system. Exploiting this fact, we show that the random open system admits a unique (meaningful) absolutely continuous conditionally stationary measure. Moreover, we prove the existence of a unique probability equilibrium measure supported on the survival set, and we …

Markov Extensions for Dynamical Systems with Holes: An Application to Expanding Maps of the Interval

We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are absolutely continuous with respect to Lebesgue measure (abbreviated a.c.c.i.m.). We develop restrictions on the Lebesgue measure of the holes and simple conditions on the dynamics of the tower which ensure existence and uniqueness in a class of Holder continuous densities. We then use these results to study the existence and properties of a.c.c.i.m. for expanding m…

马尔可夫链收敛性的谱理论刻画

Spectral theoretic characterisation of Markov chain convergence

本文通过构造周期微分算子序列，利用态密度刻画马尔可夫链的绝对连续不变测度，并给出显式收敛速率，应用于 logistic 映射、帐篷映射和 Chebyshev 映射等。