论文标题
马尔可夫人和汤普森单人$ f^+$
Markovianity and the Thompson Monoid $F^+$
论文作者
论文摘要
我们介绍了一种新的分布不变性原理，称为“部分传播性”，该原理源自汤普森单型$ f^+$在非共同概率空间中的代表理论。我们表明，非交换随机变量的部分可传播的序列适用于局部马尔可夫过滤。相反，我们表明，一大类非交通式的固定马尔可夫序列提供了汤普森MONOID $ f^+$的表示。在经典概率空间的特定情况下，我们到达了一个固定的马尔可夫序列的de finetti定理，该序列具有标准borel空间中的值。
We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid $F^+$ in noncommutative probability spaces. We show that a partially spreadable sequence of noncommutative random variables is adapted to a local Markov filtration. Conversely we show that a large class of noncommutative stationary Markov sequences provides representations of the Thompson monoid $F^+$. In the particular case of a classical probability space, we arrive at a de Finetti theorem for stationary Markov sequences with values in a standard Borel space.
