复合泊松分布用于随机动力系统：基于概率近似的方法
Compound Poisson distributions for random dynamical systems using probabilistic approximations
AI总结：
本文通过概率分块近似，对一类随机动力系统证明了淬灭击中分布为复合泊松，采用退火Kac归一化，并应用于随机分段扩张系统，揭示周期与非周期点二分法的新视角。
摘要：
我们针对一类特定的随机动力系统，获得了淬灭（quenched）击中分布为复合泊松分布的结果。该理论具有一般性，旨在适应非均匀扩张行为以及目标区域与均匀性失效区域重叠较少的情形。基于退火（annealed）和淬灭多项式相关衰减，我们的淬灭结果采用退火Kac型时间归一化，并发现极限与噪声无关。该技术涉及一种概率分块近似，其中淬灭击中计数函数在退火Kac归一化时间内被分割成大小相等的块，这些块通过一组独立同分布的随机变量来模拟。由于存在一个结果允许从返回量中恢复某些击中量，该理论得以实际应用。我们将此应用于一类随机分段扩张的一维系统，为众所周知的确定性周期点与非周期点二分法、其通常的极值指数公式EI=1-1/JT^p(x_0) 提供了新见解，并恢复了一般伯努利驱动系统的Polya-Aeppli情形，但在其他情况下则表现出不同行为。未来及正在进行的研究旨在构建并容纳真正的非均匀扩张随机系统以及目标接近其中性点的例子。
英文摘要：
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with the region where uniformity breaks. Based on annealed and quenched polynomial decay of correlations, our quenched result adopts annealed Kac-type time-normalization and finds limits to be noise-independent. The technique involves a probabilistic blockapproximation where the quenched hit-counting function up to annealed Kac-normalized time is split into equally sized blocks which are mimicked by an independency of random variables distributed just like each of them. The theory is made operational due to a result that allows certain hitting quantities to be recovered from return quantities. Our application is to a class of random piecewise expanding one-dimensional systems, casting new light on the well-known deterministic dichotomy between periodic and aperiodic points, their usual extremal index formula EI=1-1/JT^p(x_0) , and recovering the PolyaAeppli case for general Bernoulli-driven systems, but distinct behavior otherwise. Future and on-going investigations aim to produce and accommodate examples of bonafide nonuniformly expanding random systems and targets approaching their neutral points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
